I want to know if I should plan to catch one before winter break is over.
The chances of encountering Toxicroak are 1/32, or 0.03125, or 3.125%. It is available after you get the National Dex blah blah blah and can appear at any time of day. In Platinum it is the rarest post-National Dex encounter. It shares this drastically low encounter rate with Tangela, Tropius, and Yanma.
It's also been asked here.