The early days of the Winter War between the Soviet Union and Finland did not create any larger ripples in western media nor any response from the people, the military or the politicians. Most expected Finland, a poor, sparsely populated country at the outskirts of Europe to fall quickly to the Soviet juggernaut - especially as the strongest potential ally and protector of Finland, Germany, was at this time allied with the Soviets through the Molotov-Ribbentrop pact.
However, the Finnish army was very well trained, well suited to winter warfare and using its native terrain against the enemy and not only stopped the Soviets, but started scoring remarkable victories against the Soviet forces. The Finnish infantry docrine, derivated from the late German ww1 one fit like hand in glove fighting a cumbersome, road-bound and by the purges rendered initiativeless Red Army (some sources likens the Red Army at this time to a heavily armed mob rather than an army due to the lack of initiative, communication, command, control and recoinnasance.
General anti-communism in the west, the lack of any news to report from the Western Front as it was locked in the Phoney War, waiting for Spring and the status of the Soviet Union as ally of the Germans as well as the image of David versus Goliath all aided into creating a huge interest for Finland and its struggle in the world.
Despite the Germans doing their best to prevent aid to Finland to keep their Soviet allies pacified (and the raw materials they were dependent on flowing), blocking shipments of weapons, fighters and volunteers from Italy and Hungary, Swedish, French, British and US materiel arrived in large quantities (US materiels mostly arrived too late to take part in the Winter War, though).
Sweden, having old historical ties to Finland (Finland being an integral part of Sweden between about 1200 and 1809) and fearing both the Soviets and having a historical enmity with Russia, sent the most aid.
This included:
860 pistols.
85 900 rifles and carbines.
82 machine guns.
434 light machineguns.
45 000 000 small arms rounds.
2 AT rifles.
36 20mm AT guns.
114 37mm AT guns.
34 medium mortars.
147 000 medium mortar shells.
68 light field guns.
4 mountain howitzers.
12 heavy field guns
12 heavy field howitzers.
4 siege howitzers.
130 000 artillery shells.
12 dual AAMGs.
8 20mm AA guns.
72 40mm AA guns.
13 75mm AA guns.
7 obeselete biplane fighters.
12 biplane fighters.
5 biplane light bombers.
3 biplane recon planes.
5 transport, ambulance and liason planes.
9 000 volunteers with another 12 000 being accepted and under training when the war ended.
Other support includes mines (both sea and land), torpedoes, helmets, uniforms, firewood, military tents and tent stoves and above all credit for the Finnish state guaranteed by the Swedish state, allowing it to import anything it could.
Sweden had an army corps of two reinforced divisions placed along the Swedo-Finnish border, roughly 100 000 men. On the 26th of February 1940, the Finns officially asked Sweden for military aid. The Germans applied maximum political and diplomatic pressure on Sweden, and Sweden said no, but prepared to send two divisions and all their equipment as volunteers. As the Germans learned of these plans, the German military attaché in Sweden, von Uthmann threatened a German declaration of war over the issue, and the Swedes instead focused on attempting to help negotiate a peace.
At the same time the Western Allies did plan to send an expedition across Norway and Sweden to aid the Finns. The size of this expedition varied in various pland and diplomatic talks, from 6 000 men to 50 000 men (and in some speculation up to 200 000 men). On the 29th of February 50 000 men were offered "in March", which would land in Narvik, pass over the ore railroad through Kiruna and Luleå in Sweden, then go to Haparanda and enter Finland at Torneå/Tornio, regardless wether the Norwegians and Swedes approved or not.
The main part of the Western Allied plan, however, was not to aid Finland, but rather to occupy the Swedish iron ore mines at Kiruna, the iron ore railroad Narvik-Kiruna-Luleå and the ports of Narvik and Luleå to deny the Germans the Swedish iron ore, which they at this point in the war was dependent on for their steel production (and thus arms production). The Swedes knew this, as did the Germans. The German military attaché warned Sweden that Germany would intervene if Sweden allowed Western Allied troops on its soil without resistance - again threatening war.
The bottom line is that Sweden considered intervening, but decided not to due to German threats and pressure, and France and Britain were unable to secure a way to transit troops (and were more interested in using it as an excuse to occupy the Swedish iron ore mines at Kiruna) before the war ended. Germany threatened to invade Sweden should Sweden join the war against the Soviets or step up the aid beyond volunteers and equipment (sending regular troops as volunteers).
Sources:
Kriget kommer! Den hemliga svenska krigsplanläggningen under vinterkriget 1939-1940 (The war comes! The secret Swedish war planning during the Winter War 1939-1940) by Arvid Croneberg
Liten kugge i stort spel - en stabsofficer berättar (Small cog in a big game - a staff officer speaks) by Leo Wikman.
Sveriges militära beredskap (Sweden's military readiness), collected reports by the British and German Military Attachés to Sweden, Sir Victor Mallet and Bruno von Uthmann 1939-1945.
Andra världskriget och Sverige (The Second World War and Sweden) by Jan Linder.
Svenska kryptobedrifter (Swedish decryption deeds) by Bengt Beckman.
Ofredens hav, Östersjön 1939-1992 (The Sea of War, the Baltic Sea 1939-1992) by Jan Linder and Lennart Lundberg.