i dont have any experience with heated floors, but if you decide to not do them, you can get bathroom vents that also include a heat blower so you dont have to run the whole house warmer when you are showering in the morning.

While you won't hear this often, accidents happen and plumbing does go awry. Get lots of insurance and you will be very happy and secure.

Electric heated floors are perfect for this type of scenario! Simple to install and easily maintained (no moving parts and no risk of water damage as adivra mentioned).

http://www.warmquest.com/radiant-heat-products/floorizwarm

One of the most reputable systems = Ditra. It is expensive but it is an "all in one" type of product. Ditra is a well known brand name in bathroom/wet area "protection" (the water protection that sits underneath tiles in bath and showers). When working with Ditra heating systems you get everything "together" which means you know everything is compatible with everything else. The tile setters swear by it because it is very easy (No brainer as they say) to work with.

Of course, I prefer a cork glue down tile instead of heated floor. Cork will offer the same "warmth" as the (ick is right) carpet while adding thermal insulation AND a low slip surface. Mind you, I am biased to my own product.

A cold floor above a garage = something more than just "tiles". Either work with a heating system or work with something warm like cork (you are removing carpet so I won't mention it).