You can't clean yourself, but you can hide.
The description for scent says that the creature with scent can "detect opponents by sense of smell". It doesn't say "Can detect dirty opponents by sense of smell". As mxyzplk points out, the reindeer can probably smell you from 60 feet away instead of 30 if your halfling has a "strong" scent (which it probably does: smoke counts as a strong smell). So it might help to clean your clothes, but it wouldn't make you undetectable. One other concern, prestidigitation cleans "items" in a 1-foot cube. I'm not sure if prestidigitation would get the smell out of your hair or off your skin.
On the other hand, you can also use prestidigitation to soil items. And false, powerful odors can easily mask other scents. From the description of scent linked above:
False, powerful odors can easily mask other scents. The presence of such an odor completely spoils the ability to properly detect or identify creatures, and the base Survival DC to track becomes 20 rather than 10.
So you could soil a leaf or snowball, and the reindeer wouldn't be able to smell you and would have a hard time tracking you. It would need to make a Survival check of 21 (with the +1 modifier to track a lone Small creature - there's a link in the description for scent) to track you. If your GM is feeling generous, the reindeer might need to make a new check for every soiled snowball it passes, since it needs to make a new Survival check every time the tracks become difficult to follow (as per Survival rules). Don't soil more than one snowball at a time. Strangely, scent only works on opponents or via tracks, but if you leave a trail of soiled snowballs, that probably doesn't count as a false smell. But you could change direction and soil a new snowball each time the reindeer seems to be getting closer to you.