I’ll conflate these two topics in one post because I really don’t have much to say about either in the context of winter houseplants. And I seem to prefer long posts…
I’ll go out on a limb and claim that most people probably keep their houses/apartments somewhere around 18 or 19 °C in winter, give or take a few degrees (I keep mine at 19°). For the vast majority of houseplants, even most tropicals, this is tolerable. Only a few will demand significantly higher temperatures just for survival. Even I wouldn’t suggest you should heat your home to the point it becomes uncomfortable or uneconomical for the sake of a few extra-fussy houseplants.
If you do keep such plants (and right now I can’t even think of any…at least, any that are legal around here…), you’ll probably have to fuss around with lamps, space heaters, Wardian cases, and the like.
It is important, though, to keep the temperature fairly constant. Plants don’t appreciate hot or cold draughts any more than we do, so try not to put them where cold air blows in from the front door, or under/over an air vent.
As for fertilising, well, don’t. Houseplants slow down their growth in winter and they just don’t need the feeding. Chemical fertilisers especially could build up in the soil to toxic levels. At most, fertilise at half strength and double intervals; if in doubt, err on the side of stinginess.
Organic fertilisers are much gentler and if you have any left over from summer, are a better bet if you feel you must fertilise in winter. There is limited space in a container to add compost or manure, of course, so liquid forms are easier to use. Compost tea, manure tea (neither is as bad as they sound), and comfrey liquid (which is a lot worse than it sounds) are good ones at any time of year. Just dilute them more in winter.
Take this with a grain of salt, of course – if a particular plant IS growing away nicely and steadily in winter, then a bit of judicious fertilising might well be in order. And if you’re trying indoor salad crops (arugula does pretty well in a sunny window, for example), a bit of feeding for them wouldn’t be unreasonable either.