I have a few small areas to paint. I can do them during the day when
it's 40F, but overnight it will drop below freezing. Is that a
problem? Do I just need to wait until spring?

I have a small bit of siding on a dormer and a bit of trim. I can
easily get it painted in 40F and it will have a few hours to dry, but
6 to 8 hours later it's likely to drop below freezing.