I always put the top on my MGs down in April, and up in October. I learned the hard way, when I didn't get around to putting the top up until December. Never again! I had to put a heater in the car with the top partially up to warm it up enough to get the top in place and properly snapped.
I have stored them over the winter with the top down, but as said above, I think it holds its shape better when up. Especially thru the cold months. The folds seem to crease more when they go thru the cold months in the folded condition.
Just 40 years of lessons learned, sometimes the hard way.