As a Finn whose father was on the front I say, not much to be embarrassed beyond acting in national interest. Thank you for the 8500 men in 1939-1940, 33 of whom were killed, and for the Svenska Frivilligbataljonen later.
(Plus thank you for the kind act of accepting thousands of small children as refugees, even if in the end it turned out to be not such a good idea to split families; the lesson is that don't do that as a temporary relief; if you must give children away, let them be adopted.)
The Swedish organized force (not individual volunteers) for the Winter War was trained, organized and at the front just as the peace started, so they missed most of the blood letting.
We talk about sending a 1/3 of the Swedish military equipment, including of the air force. (Sadly not enough, the politicians had been doing downsizing defense -- just as they have now, when Putin is starting to act like Hitler in the 1930s.)
Wikipedia claimed this aid was the politicians' way of silencing a popular opinion that Sweden should do more. I don't really know. I do know that Swedes in general have no clue about the subject, after the education.
Also, a disclaimer -- I am half Swedish and half Danish, with half the Swedish relatives from the Finn forests of Värmland. So I really don't have a horse in this race. (When Finns have problems with Swedes, I tell them about my relative in Norway 300 years ago, which became a general major by killing lots of "you damned Swedes and Finns". :-) )
Yes, it was a really significant thing, tightroping between how much Sweden can support Finland without becoming an outright adversary of USSR and its allies (first Nazi Germany, then Britain and USA).
(Plus thank you for the kind act of accepting thousands of small children as refugees, even if in the end it turned out to be not such a good idea to split families; the lesson is that don't do that as a temporary relief; if you must give children away, let them be adopted.)