First off, whether I shovel or kick aside any snow depends on the conditions. If there is a lot of snow and you clear it off all the way down to the ice, then water can come out of the holes and leave you with a nice little lake inside the shelter. I see onestring has mentioned this just now.
Next, I've gone to placing the heater on a small wooden crate. As mentioned, that stops the floor melt immediately in front of it.
Lastly, floor mats slide around less for me if they are on snow instead of directly on ice.
YMMV