Yes, you can paint the windows white, unless the existing dark brown finish is some form of oil that won't accept paint.
Lightly sand back the existing stain or varnish to provide a key for the new paint, fill any defects with a suitable wood or all purpose filler, sand flat, wipe clean and you are ready to go.
As the windows are hardwood, you will need a primer that will act as a block for resinous bleed. Aluminium primer or Zinsser Coverstain are ideal products for this and will stop red/orange streaks from leaching through your finish coats. Some varnishes will act as a block providing you don't sand them back too far and a standard oil based undercoat can often stop resinous bleed but, to be on the safe side, I would use either of the above products to be sure.
The type of paint to use will depend on your preference. Oil based paints are traditional for timber, and have better longevity on exterior surfaces than their water-based counterparts, but they are not as nice to work with as they used to be and can discolour rapidly, especially internally. Water based or hybrid paints are being used more and more to keep the whiteness but are not as hardwearing. Have a read through some other threads and you should find some good info on them.
Sikkens seems to be well rated for exterior surfaces, but I have to admit that I tended to stick to traditional brands until I stopped painting, so can't give an honest opinion on their products.
