Yep, the Snow's audio inputs are a competent ASIO soundcard, so you wont need another dedicated one. In fact from reading others' posts on here and other places people have been surprised at the quality of the inputs on the Snow/TI.
The only drawback really is that the Snow and the audio inputs are limited to 44.1KHz @ 16-bit when using the USB connection alone. But it shouldn't really be too much of a problem.
Logic... looks great. I would have used Logic myself if it was still available for PC, as the standard plugins in Logic are far superior to Cubase. As I use a PC, I'm getting used to Sonar instead.
Never tried nor know much about DP as I haven't a Mac. The MIDI automation user-interface in DP looked good, merely judging from photos however.
Either way, I think you'll like the TI Snow.
Sound quality wise, it's a big step up from soft-synths.