I heard that interior painting is not a very good idea during winter. How accurate is this statement and why?
Absolutely not accurate!!!!!! There is no reason not to paint inside as long as temps are above 60F. Today's latex acrylic paints dry fast, adhere well, and apply well in moderate temps.( we always use some flowtrol to make it work longer and spread smoother) Actually, in winter the relative humidity is usually lower, so paint dries faster than in the heat and humidity of summer. Longer dry times lets more dust adhere. Go for it during the winter, then you will have more time to enjoy the out of doors come summer time!!!!
Temperature and humidity can affect how well the paint adheres to the surface being painted. I imagine that using a low-quality paint in a humid environment could create a problem, especially if trying to apply multiple coats.
Quality paints (and paint is, in my experience, something to spend the money on) have pretty wide tolerances though; I wouldn't hesitate to paint in the winter.
All paints have a range of temperatures and humidities at which they work best and you may experience problems with it taking longer for the paint to dry etc. if you work outside these ranges. This applies to high temperature as well as low temperature, though it's usually high humidity that's more of a problem (as shirlock mentions).
So check the data on the side of the can to see what the manufacturer recommends. If you're concerned that the temperature might be outside the range try a small area (or paint a spare board) and see how well the paint goes on and how long it takes to dry before tackling the whole room.
If the paint you have does cause you problems and you really have to paint in "extreme" conditions go back to the store and see if there's a different kind of paint that meets your requirements.
The main problem I find with painting during winter is the shortness of the daylight hours. I find it difficult to get even and complete coverage of wall and ceilings in artificial light so I much prefer painting in the spring and summer.