I'm pretty sure it is legal for private ownership of antivenom, but it doesn't make much sense unless you're planning on getting bit soon - as mentioned it has a finite shelf life. The private owners keeping it are either really wealthy or getting it illegally.

There also isn't a lot out there for purchase and a lot of it is still being created/tested since there aren't antivenoms for all species. Not to mention it can have a very negative effect - as mentioned, it can cause an allergic reaction worse than the venom itself. If self administered for a dry bit (or even a wet one) you could kill yourself with it.

Also, as mentioned, it is very costly - I believe around $1,000 a vial when administered at a hospital and you can expect to need 15+ vials for many bites. Idk about you, but owning a hot and getting a bite isn't worth $15k - that doesn't mean don't get any, just do your research and be properly prepared.

Definitely check for the nearest hospitals that carry the necessary antivenom - the last thing you want to be doing when you get bit is calling around or looking in the yellow pages