I have a 1999 Jetta TDI.
I'm in the habit of putting the key in and just turning it. In the winter, there's a little light on the dash, and you need to turn the key halfway, wait for the light to go out, then turn it the rest of the way to start the car. If you don't do this, it will take a few seconds to start.
Another possible issue is the fuel gelling. This is fairly rare - it has to get really cold for it to happen. Different states/provinces sell different blends of fuel in the winter time (i.e. fuel sold in Michigan won't gel until it gets to a lower temperature than what would cause fuel sold in Florida to gel). The intention there is to make it so that your fuel won't gel.
For the 10 years I've owned my car, it's never gelled. I've lived in central Indiana that whole time. I park in the garage at night, though. If you don't have a garage, it's possible it might gel like one morning per year.
One more thing about the different states' formulations: since these cars can go so far on a tank, say you live in Detroit and go on a trip down South, during the winter, and on the way home you fill up in Lexington, KY. When you get home, you'll probably still have half a tank of Kentucky-formulated fuel in your car. It would probably be a good idea to fill the tank the rest of the way with Michigan fuel.
They sell engine block heaters - you glue it onto the bottom of your engine (quick and easy, just have to jack up the car then remove a plastic cover on the Jetta to get to it). I think they're like $60. If you don't have a garage, but do have access to a power outlet, then on the coldest winter nights you can just put it on a timer to start heating a couple hours before whatever time you leave in the morning, and you should be good to go.
Get the car - they're excellent. I should hit 200,000 miles sometime in June. My window sticker said 49mpg highway...when I drive normally (80mph) I get about 46mpg and when I drive like an old lady I get up to 53mpg. Even at 10 years old, it's still nice and peppy. Any problem you ever have, you can find lots of helpful people at forums.tdiclub.com