What zone are you in? Here in zone 5, even in the hoophouse the ground eventually freezes. It just buys additional time.

You should be able to wait until a couple weeks (2-4 weeks) before your intended planting to put up the covering to pre-warm the soil and help dry it out if it needs it.

And it helps to allow the soil to be exposed to the elements (so long as erosion isn't an issue) when you can. The cold helps to discourage pests from thinking it's their winter palace.

An additional benefit in waiting to cover your hoophouse is extending the life of the plastic covering.

I do the same thing as you. But, I agree with what has been posted.

Reasons to leave it uncovered for the worst of the winter:

1) Discourage pests.
2) Extends the life of the plastic by exposing it to less UV light.
3) Don't have to worry about snow buildup on the top of the hoop house.

If you are worried about the soil freezing too deeply without the hoop house, simply put down a thick layer of mulch. Remove the mulch before putting the hoop house back in place and the soil will warm more quickly. Then, return the mulch once the hoop house is no longer needed to warm the soil.