Perhaps your ancestors were among the children evacuated to Sweden during the war. A massive number of Finnish children were sent to safety in Sweden as the war raged on and the government feared for the children's safety during a theoretical Russian occupation.

Here is an English language radio program that deals with it, by the Swedish national radio broadcasting corporation's website: http://sverigesradio.se/sida/artikel.aspx?programid=2054&artikel=1081470

(Hopefully it'll work outside Sweden, but you just tell if it doesn't)

I have to say I haven't heard of such and while I don't doubt many people (not just in Finland) had their doubts about bringing children into the world at war, this didn't seem to have much effect on population growth. Most noticeably, number of births rebounded in 1941 due the short "interim peace" (March 1940-June 1941), which would seem to disconfirm the notion that fear of another war would've been a major factor in a decision to have a child.

However, what did have an effect was that most males were at the front; this depressed fertility rates noticeably (with obvious nine-month lag of course) but also contributed to a post-war baby boom once the men returned. The greatest spike in baby births was experienced exactly nine months after the general demobilization that began in early December 1944, in August and September 1945.

I checked the official statistics at Statistics Finland and here's the results in live births per year for the relevant period.