We're considering going in January. It will be cold in Madrid, but moderate in the south, and crowds are light.
I went to Barcelona in January 2017 and it wasn't bad at all weather-wise - coolish with occasional rain. I also went to Estonia in March 2015 and got a little of everything, from almost-balmy clear days to full-on snow.
If all continues to go well I'm off to Lithuania this coming Wednesday - for a week, and yesterday I checked weather.com and they've got showers predicted for every day I'm there...thing is though, they said the same thing about an earlier trip I took there and it turned out there was rain on only one day of the six I was there.