If one is unable to sleep in the Sukkah due to cold weather, one is not obligated to do so, and one is not obligated to take extreme measures to create a warm Sukkah to enable himself to sleep in the Sukkah. (Shulchan Aruch w/Mishnah Berurah 639:2, Moadim U’zmanim 8:Hashmotos to Chelek 2:107)
Nevertheless, since “one who removes himself from the Mitzvah of Sukkah – his punishment is great”; and nowadays one can easily install a heater to alleviate a moderately cold night, one should make the extra effort to do so, when and where possible. This was the custom of the Chofetz Chaim and R’ Chaim Brisker. (Piskei Tshuvos 639:7, Mishnah Berurah 639:MB31, S’U Min Hashomayim 11, Sukkah Hasholaim Miluim L’Perek25, Nimukei Orach Chaim 639)
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what kind of heater is safe to install outdoors in a sukkah?
Probably the safest way a propane or kerosene space outdoor space heather, but they can be pricey (usually about $100 or more, plus the cost of the fuel).
Last year we had an electric space heater. I was careful to use an extension cord rated for greater than the wattage of the space heater and put a small “roof” of aluminum foil a few feet above the space heater to protect from the rain (you should not put it directly above, but need to leave space for the heat to escape as most space heaters will warn “DO NOT COVER”).
That said, it was not very effective and only provided warmth if you were standing immediately next to it, plus it was hot to touch so dangerous for small children.
I think if you can get a gas-based outdoor space heather that would be the best option and set it up safely (with proper ventilation for the fumes, etc.) that would be the best option.