Obviously you can light a fire on the snow but it will quickly melt the snow, sink into it and go out. And this is just when you most need a fire, so what to do? Find somewhere clear of snow is the easiest choice: often there is little or no snow under trees. It is anyway easier to clear a space down to the ground there, being sure to shake down snow from overhead branches as well. As you pile up snow to the outside it may also be possible to create a tipi-like (windward) shelter with a dry floor out of branches laid against the trunk to enhance the warmth of the fire (but be sure not to suffocate yourself).
If the snow is very deep you will need some kind of platform for the fire to rest on. Lots of folks suggest stones – but they are likely a long way down in this circumstance, and you are likely cold and in a hurry. A raft of wet wood is the best idea, the thicker the better, then you proceed to light the fire in the normal way starting with tinder and the smallest driest pieces and working your way upwards. Have all your fire materials ready assembled before you strike the first spark: you definitely may only get one chance at this – and it may well be your last! Follow the instructions here: http://www.theultralighthiker.com/how-to-light-a-fire-in-the-wet/ and here: http://www.instructables.com/id/Building-Campfires-the-Right-Way-without-Fire-Star/?ALLSTEPS See also: http://www.outdoorlife.com/blogs/survivalist/2013/03/survival-skills-how-build-fire-snow & http://www.offthegridnews.com/extreme-survival/the-simple-way-to-start-a-fire-in-the-snow/ & etc…
PS: ‘Fire on the Snow’ was the title of a great radio play by the (late) Australian poet Douglas Stewart about the ill-fated 1912 Scott expedition. You can listen to it here: http://trove.nla.gov.au/work/11851529