It is perfectly fine to be at home, as long as you can make the effort to keep moving about, stand up, sit down, move around. There was a local pavement black ice warning yesterday, on fb, I am also cautious. I found my old walking trainers (merrill) and they gave me added security earlier this week. Slippy shoes, definitely not
The winter before I moved here, I stood outside my front door and my feet went from under me. The impact with the ground is very hard when that happens, luckily I sat on a patch of snow but it was still sudden and hard
No need to feel guilty or silly about staying at home, at least you wont be one of the ones in hospital with a broken hip or arm. Just find something to do, even if only clearing a cupboard or a drawer. Also do vary your day and eat well