Also, how did the technology of the two compare and how useful was Soviet armor in the snow and cold weather. Why was the Finnish army so good?
The winter war isn't quite my area of expertise, it's kind of adjacent though, so I'll heavily lean on journal articles and books for this.
Soviet forces performed dismally in the initial offensive operations during that war. Offensive preparations were poor, coordination of forces weak, and command and control ineffective. Consequently the first offensive failure was a major embarrassment. Only after more extensive mobilization and intensive preparations was the Finnish defense crushed.
David M. Glantz, Soviet Military Operational Art p. 91
On 30 November 1939, 9th Army formations (54th, 122nd, and 163rd Rifle Divisions^4 ) crushed the Finnish border outposts and advanced swiftly. The Finnish command was able to concentrate 5-6 battalions with a few mortars and artillery against them. In view of the Soviet forces' significant superiority, the Finns waged only containment battles at earlier prepared positions, and gradually withdrew into the depths of their territory. During these battles they stopped the pursuing Red Army formations for several hours, and then continued to withdraw, destroying bridges and constructing barriers on roads.
General I. Siilasvuiu, 9th Infantry Division commander, recalled, 'It was strange and incomprehensible to me why the Russians had no skis and, therefore, could not leave the roads. They suffered heavy losses because of this.'^10 In fact, the lack of skis and the inability to ski on the part of personnel not only from 163rd Rifle Division, but also from all other Soviet divisions (except for 54th Mountain-Rifle Division) resulted in the fact that the regiments were able to move only along roads, and the deep snow made it impossible for units to move off the roads or maneuver in any way. This greatly contributed to the success of the mobile Finnish ski detachments: it made it possible to make unexpected attacks from the flank and into the rear of Soviet units, and to easily avoid pursuit in case of failure.
Emphasis added. The Finns fought a dogged defense in depth, and the Soviets had persistent C2 and organizational issues, as well as mobility issues, which the Finns exploited. This, I think, is part of why they held on for so long. The Soviets were unable to exploit their armored advantage, as the terrain in the region is rather hard to move in. Telling is the report written by Maj. S. G. Chernov, quoted in Aptekar and Dudrova "The Unheeded Warning and the Winter War" Journal of Slavic Military Studies V. 10 No.1 (March 1997) P. 207
The role of 9th Army and its missions are understood correctly by the army command, but the decision is built on the fact that the enemy will not offer resistance... The operational tempo was planned for an average of 22 km per day, at a time when our forces were moving 12-16 kilometers per day toward the border, with units being spread out and equipment (mainly artillery) lagging behind. How, then, can such a tempo be planned for enemy territory?! This means to build an operation on sand, without a real condition or front features. In the calculations, the enemy was not taken into account, nor was the lack of roads considered, this is a gross operational miscalculation, and later this may be at the cost of thwarting the entire operation at the very beginning, especially if the enemy offers resistance by means of obstacles and covering them with border units, not to mention bringing up field forces... All their lines of communication will be cut by enemy diversionary groups, and they will be without food or ammunition; Finnish tactics will basically boil down to this... It is necessary now to create in divisions detachments of good skiers and to concern ourselves with providing skis to all divisions. It will be very bad without skis, they will not be able to leave the road, but will meet the enemy (head to head) and this will delay movement very much.
Emphasis added. Chernov mentioned in the margins,
This haste may end badly, the operation has not been thought out, I don't know about the other armies, but this may be thwarted, especially with respect to 9th and 8th Armies.
Let's now draw our attention to excerpts from the curricula of the Voroshilov General Staff Academy 1977 history textbook, to get a view of why the Soviets thought they lost the war. David M. Glantz, "Excerpts on Soviet 1938–40 operations from the history of warfare, military art, and military science, a 1977 textbook of the military academy of the general staff of the USSR armed forces" Journal of Slavic Military Studies Vol. 6 No.1, March 1993,
At 0830 on 30 November Leningrad Military District forces crossed the Finnish border. Thus began military actions between Finland and the USSR. Although ordering its forces to attack, the Soviet government had no intentions of seizing Finland and depriving it of independence. Rather, it strove only to put an end to using this country as a bridgehead for anti-Soviet forces. (p. 122)
Since ancient times Finland has been renowned as the 'country of forests and thousands of lakes.' There are more than 30,000 lakes in Finland, and they occupy 12 per cent of its entire territory. Forest tracts encompass 74 per cent of the country's entire area. If to this are added numerous rivers and very rugged terrain covered by deep snow, rocky ridges, cliffs, and enormous boulders, then it is easy to imagine how natural conditions have made Finland inaccessible to invasion from the east. The terrain was so advantageous for defense that even its insignificant reinforcement with field fortifications provided an enormous advantage to defending forces. Natural conditions seriously impeded movement and maneuver of large formations, and created extreme difficulties for the attacker. Red Army forces had to fight under conditions of a cruel winter, in deep snow, with no roads, often in dense fog, under conditions where it was impossible to employ modern combat equipment and weapons with adequate effectiveness (p.123)
At 0830 on 30 November 1939, following a 30-minute artillery preparation on the Karelian Isthmus and a 15-minute artillery preparation on the remaining axes, Soviet forces crossed the Finnish border. For several reasons the Soviet-Finnish conflict did not progress in full accordance with the Soviet command's plans and recommendations. (129)
Possibly the understatement of the century there. Like damn.
Limited results and the incompleteness of planned Soviet operations can be explained by the fact that they were not prepared beforehand for actions to penetrate fortified regions. Our military theory had not adequately worked out forms of combat actions under special conditions. Thus, in Provisional Field Regulations-36, only one article (212) was devoted to the offensive against a fortified region; this stated: 'The offensive against fortified regions or sectors is conducted on the basis of special instructions.' However, such instructions had not been developed.
In the plan for Field Regulations-39, nine articles were allocated to the question of penetrating fortified regions, but they did not receive adequate clarification. The situation was analogous with the problem of an offensive in a forest and forested-swampy terrain covered with lakes, as well as in the inter-lake defiles, under severe winter conditions.
The experience of combat actions against Finland in 1939-1940 had enormous significance for the development of Soviet military art. On this basis the Soviet Army began to create its theory of penetration of a fortified region
Combat actions in the Northwestern Theater demonstrated the Soviet command's ability to concentrate overwhelming forces and means on a selected principal strategic axis (Karelian Isthmus) and subordinate the actions of all armed forces services to the primary mission - the rout and destruction of the main enemy grouping
The penetration of the Mannerheim Line using all modern combat means was a unique phenomenon. This was the first experience in the world of such a front operation. Dynamic actions of Soviet forces on other operational axes on the enormous Soviet-Finnish front were closely coordinated with its concluding stage.
It was established that it was expedient to penetrate a reinforced defense in a narrow front sector with a deep force combat formation by successively capturing separate defensive objectives with powerful means of destruction and suppression; a plan worked out in detail and especially careful preparation were necessary. Practical combat experience in Karelia confirmed the correctness of methods of artillery support of the troop offensive, which consisted of artillery preparation, support of the attack, and accompaniment. The most effective method of attack support was an artillery fire barrage, sometimes in combination with successive fire concentrations. Combat experience in Finland was reflected.in the new draft Field Regulations 1940, and in a number of instructions and manuals on troop combat preparation. It was the subject of intensive study and generalization at the 1940 March Plenum of the Party Central Committee, and at a meeting of the Main Military Council in April 1940. Troop combat readiness was increased on the basis of decisions made by them, and combat training approached actual war conditions
So, in summation, what were the Soviet flaws? Limited mobility, persistent command and control issues, and fighting in terrible conditions which heavily favored the defender. Even still the Soviets were able to achieve their aims and then some by peace treaty. Given the actions of the Finns during '41 in the march on Leningrad the border movements as a result of the Winter War shouldn't be underestimated.
Hopefully this is a somewhat complete answer to your question! I'm running up against the character limit, but feel free to ask follow-ups!