If you have the shed well insulated, the snow on the roof shouldn't melt off. The insulation will keep heat in and the cold out. Depending on how close the neighbors are, carbon filter is optional, that's up to you and if smell is a problem because of how close neighbors are. Here's what I would do, it sounds like your shed is pretty well built. I would get a space heater that has a thermostat built in it. I got one for around 75 bucks I think. You can set it for 60-80 degrees and it only runs to maintain the temp you set it at. Put that outside the tent in the shed. Leave Windows closed. Have the heater set next to the tent and have a small booster fan in one of the bottom air ducts on the tent. Carbon Filter inside the tent like this.
Filter>light>duct out of tent into shed. This will scrub the air and put the heat from the light into the shed making a nice ambient temp in the shed while lights on. The thermostat space heater will keep plants warm when lights off by using the small booster fan blowing the heater heat into the tent
Also, make sure neighbors don't see a bright light shining out the shed window. If smell is an issue, that means you have close by neighbors, so black out the shed Windows so when you open the tent the light can't be seen