All world cups as we know are held in the summer, but there could be a big advantage in a winter world cup, with the demands of modern football, by the time the summer tournament arrives, most players are tired, some carrying injuries, some injured outright, so we never get to see the top quality players at their best. Having the tournament in winter could change that, players are still more fresh than they'd be in the summer, and we could possibly get a far more exciting tournament as a result of that. That's one big advantage of a winter world cup. Just look at how dire the last world cup was, the world cup in South Korea-Japan hardly set the world on fire either, 2006 is the last world cup I remember as being entertaining, but even in that tournament there weren't a lot of top quality games.
The trouble with holding it in the winter is that it will have a huge impact on the domestic season. There's talk of extending the PL to play in June and July to compensate, which will mean that players who play in the tournament will be absolutely knackered come August when another season starts. As cym said, it was probably one of the worst decisions FIFA made to award the tournament to Qatar and not just because of the weather.