My wife put together this several winters back for an old neighborhood stray cat she kind of took a liking to and kept feed and watered. No reason why something like it wouldn't work for a up to medium size outside kept dog too.
Ordinary plastic storage bin of the right size w/lid, usually costs $10 or less,... cut a hole of the right size as a entry/exit door in one of the sides,... line the inside with something with insulating properties (IIRC she used crumpled news paper between cardboard 'walls'),... old blankets and old terry cloth bath towels for bedding.
Snow, rain, sleet, freezing rain, bitter cold, the cat used it so I guess it helped. You could probably still use the heat rock or pet heating pad too.
