Our weather is up and down here too. We can have late freezes into early May.
I'm not an expert on winter sowing but I'm sure it's ok to winter sow your perennials now.
Is it your annuals you're worried about? Some people wait until March for those but some people sow them earlier. For the most part they won't germinate until they're supposed to even when you sow them early. Some annuals need cold stratification and some don't. It's time consuming but you can research each one to find out if does. Or search to see if it's "tender"
If you have a freeze after your tender annuals have sprouted, maybe you could move those against a south wall and cover them with a tarp instead of bringing them indoors.
The containers get much warmer in the sun than they do in the shade. You can discourage early sprouts by putting them in a shadier location.
Hope that helps. I've been winter sowing off and on for 20 years(?) but I'm still learning. The weather is never the same.
