Gardening indoors in winter allows you to do your favourite hobby during the long, cold winter months. Of course, you'll need to help your plants along a little more, but it's easier than you think.
The key factors to look at in gardening are:
In winter, the last two (light and temperature) are the ones that need some more attention. You should continue to fertilize and water your plants just as you would throughout the rest of the year.
Sunlight-loving plants need a good eight or so hours of sunlight per day. If you live quite far from the Equator, your plants won't be getting this! So you'll need to supplement the sunlight with artificial lighting.
You have several options for lighting:
Don't bother with ordinary, incandescent lightbulbs. All they do is generate heat and only a fraction of light in the spectrums that plants can use.
If your home gets cold during winter, you'll need to do something to provide your plants with some warmth so that the cold doesn't stunt their growth. A comfortable room temperature should be fine.
One way you can do this is by putting your plants near a radiator but not so close that they get hot. Or you can use a light bulb type that generates some heat. So in that case, LED grow lights would be a bad choice.