If I use garage-type heaters in the attic during the winter, will this help keep snow and ice off the roof?
what would happen is that the snow or ice on the roof would melt somewhat, flow down to the edge of the roof where the attic ends, and refreeze, forming large ice dams. The ice and snow would continue to melt, backing up liquid water against the roof and evenutually finding its way under the shingles and through the sheathing into your home where it would drip down the ceilings and walls onto your dog, your kids and your computer. You would then curse and try to find a solution, but by then its too late. Your kids would hate you, your computer would be ruined.
Should you do this, when you replace your roof, put the rubber sheet material under the shingles. It is specifically designed to help prevent the ice dam issue.
The snow is a great insulator, so it would do its best to hold the heat inside of your attic space. Just mocking your attempts to melt it.
And the electric bills from the heaters would likely give you a heart attack, so then there would be medical bills.
I understand exactly what you are trying to do, but sadly physics is against you on this one.
It just kills me when there is a bright sunny day, and my solar panels are buried under 5 inches of snow.