My toddler does the same thing, I think in part it's potty learning readiness and in part it's an independence thing - she wants to put them back on herself, but gives up the second it doesn't go on easily and is happy being naked. I think most kids would prefer to be naked. If you allow nakey time at home, will she be more amenable to wearing clohes when out? We've always had a "You must wear clothes to go out" rule, and some days the promise of going out is the only way I can get DD (2) to get dressed.
At nighttime, I'd just let her sleep naked if that's what she wants - I'd say something like "OK, no jammies, but you do need a diaper, OK?" That's a compromise my DD would be OK with. And if she's cold at night, well, that's just a natural consequence and a learning experience, right?