I did this last winter. Mining 24/7 on my personal rig noticeably took a bit of load off the heater and made a modest amount of ethereum. I stopped once the weather warmed as it seemed like a waste of energy.
Not appreciably different, that was the whole logic behind my thinking. In my case I have electric heaters, so doesn't make a difference compared to a gpu -- they're both effectively 100% thermally efficient.
