The short version: astonishment and admiration, and some aid to Finland, but much less than Finland wanted.
"Astonishment" is straightforward: most of the world, including the Soviet Union, expected the invasion to be a walkover, with the Red Army brushing aside Finnish resistance. When the Soviet advance in the Karelian Isthmus stalled after a week when they reached the Mannerheim Line (the first week of the war in the isthmus having consisted of their advance to that line, with forward Finnish covering troops falling back to the line), and the following fortnight of repeated attacks achieving little other than many Soviet casualties, the world - and the Soviet leadership - was surprised. Surprise increased even more when the Finns shredded two Soviet divisions in the Battle of Raate Road in the first week of January (neither Soviet division commander survived; the commander of the 163rd Division, Andrei Zelentsov, was killed in the battle itself, and the commander of the 44th Division, Alexei Vinogradov, was executed by firing squad in front of the survivors of his division after the escaped back to Soviet territory). At the start of the war, only Finland had been optimistic about stopping the Soviets. From an article in the press, December 1939,
Finland's Heroic Resistance Surprises the World
To the surprise of the outside world, but not of the Finnish people themselves, Finland succeeded in putting up a prolonged and desperate resistance to the Russian onslaught.
Optimism in the Finnish army was partly genuine, partly naïve overconfidence, and partly deliberate overconfidence to bolster their own morale. The defensive victories on the isthmus surprised the Finns, first by the number of Soviet troops available, and second by the primitive Soviet tactics.
"Admiration" was more mixed, and lacking from the Soviet Union. As a peaceful democratic state, Finland received much sympathy, even from Fascist states such as Italy.
One thing driving these reactions was the timing: the Winter War took place during the Phony War, the quiet period of WWII between the defeat of Poland and the invasions of Denmark and Norway. With WWII, or the "European War" as it was often called at the time, not generating much in the way of news, the Winter War got prominent media coverage. The contrast between the quick defeat of Poland and Finland's successful first month of the Winter War highlighted the remarkable Finnish achievement of stopping the Soviet advance. Also related to timing, with the Soviet Union's non-aggression pact with Germany, and the Soviet invasion of Poland, the Soviet Union was easily seen as the villain - Finland was little democratic David vs the brutal Goliath of the Soviet Union. Without the Soviet pact with Germany, and without recent Soviet predatory aggression towards the Baltic states and Poland, the Soviet Union would have had more chance of portraying Finland as stubborn and refusing a reasonable request to adjust the border near Leningrad. As it was, Finland got a lot of sympathy as well as admiration.
Finland wanted a lot more than sympathy and admiration. While some of the Finnish soldiers were (over)confident, the military and political leadership were realistic. They knew that if the Soviet Union continued to attack with determination, it would end in a Soviet victory. They thought that their best chance was enough international intervention to make the Soviet Union back down, and sought serious international military assistance and intervention, and international pressure on the Soviet Union. There was some assistance/intervention, and some pressure, but far from enough to force the Soviets to stop.
There was widespread international condemnation, both by governments (first was the US president Franklin D. Roosevelt, who condemned the Soviet invasion in a speech, and offered to mediate) and by the public (there were many protests outside Soviet embassies around the world), and the Soviet Union was even kicked out of the League of Nations:
Since this condemnation had no military or economic teeth, the Soviet Union simply ignored it.
The largest amount of military aid came from Sweden. Finland wanted Sweden to join the war as a belligerent, but Sweden refused. Sweden provided generous military aid in the form of weapons and equipment, including over 100,000 small arms and over 50 million rounds of ammunition, almost 250 artillery pieces (field guns, anti-tank guns, and anti-aircraft guns) with over 300,000 shells, and 26 aircraft. Sweden allowed its military personnel to volunteer to serve in Finland, as independent volunteers rather than as Swedish troops. Of the volunteers, almost 10,000 went to Finland, and some saw combat near the end of the war. Many volunteers came from around the world, but of those who reached Finland before the end of the war, most were still training when the war ended. Apart from the Swedes, who saw combat on the front line, some Norwegian volunteers served on the front, in a quiet area (and unlike the Swedes, they had no combat casualties). The Swedish aid produced mixed feelings: there was certainly gratitude for the aid and the volunteers, but also disappointment that it was far short of what Finland wanted (which was for Sweden to join the war as an ally).
Britain, France, and Italy sold weapons, including modern aircraft, to Finland. Some of this aid reached Finland in time to be used in the Winter War, and much did not. Germany refused to allow the transit of aid to Finland (due to their pact with the Soviet Union, which included secret clauses assigning Finland to the Soviet sphere of influence), which blocked much of the aid from Italy and Hungary. The US government loaned money to Finland, on condition that it was not spent on military stuff. Private fundraising in many countries raised funds for Finland, without such strings attached. The USA, Sweden, and Norway were prominent among such fundraisers.
Britain and France offered a larger intervention. However, helping Finland was only part of their plan - their other goal was to cut off the supply of Swedish iron ore to Germany, by occupying Norway, and perhaps Sweden, if they refused to allow free passage of British and French troops. (Note that Swedish iron ore was exported through Norwegian ports, which were closer to the mines than Swedish ports, and ice-free.) It was likely that only a small part of the Anglo-French force would have reached Finland. Whether this intervention would have happened in unknown. Britain and France offered it, asking Finland to make a formal request for their intervention (to justify their occupation of Norway and Sweden). The Finnish leadership was skeptical that the intervention would translate into enough troops on the front to make a useful difference - these negotiations were taking place near the end of the war as the Finnish defences were crumbling. In the end, Finland did not make that asked-for formal request, but kept the negotiations with Britain and France active to put pressure on the Soviet Union to offer acceptable peace terms that would preserve Finnish independence. The threat of Anglo-French intervention did help the Finns - Stalin wanted to keep the Soviet Union out of WWII proper (i.e., the war between Germany and the British-French alliance).
tl;dr- overall, there was international condemnation, however the world did nothing to assist Finland.
Overall, the world was outraged with the Soviet invasion of Finland on November 30, 1939. In fact, many diplomats (including that of the US) believed that war was not coming (The Chargé in Finland (Shantz) to the Secretary of State, 18 September 1939).
When the bombs did begin to fall on Helsinki, President Roosevelt immediately released a statement of condemnation of the Soviet actions, and expressed support for the Finns. Other countries, such as Columbia, also expressed support for Finland (FDR Library Documents, PSFA0286). In the US, Herbert Hoover organized the Finnish Relief Fund, which raised the 2019 equivalent of $36.5 million in a 3 month span (Jacobs, America and the Winter War, 87). In a gallup poll from December 1939, 88% of the respondents expressed support for Finland while only 1% expressed support for the Soviets (Gallup Survey #179, Question 4A, 31 Dec. 1939). Public opinion was also not in favor of the Soviets blindly bombing Finland, where there was no concern for Military or Civilian targets.
The only countries that talked of military action were the French and the British, however their plans were derailed by the refusal of the Swedish and Norwegian governments to allow troops to pass through their borders (The Chargé in the United Kingdom (Johnson) to the Secretary of State, 4 January 1940). There were international volunteers that formed units and volunteered for service in the Winter War, from countries such as the UK, Sweden, and the US, among other places. Many volunteers did not have military experience, and had to go through training in Finland, which meant they did not see any active service. An exception to this was a company sized element of Finnish-American volunteers that saw action on the last day of the Winter War (Memoirs of Marshall Mannerheim, 363).