Is it feasible to freeze a whole pig?

I agree with the comment by Richard ten Brink: you can't really do this in a home freezer and expect good results. Even with a large home chest freezer, it will take way too long for a whole carcass to freeze all the way through. Freezing requires a lot more energy than maintaining something that's already frozen, and the process for a pig carcass would probably take several days (depending on the size of the pig). You'd likely get significant quality degradation during the freezing process itself: slower freezing means more damage to cells, which affects meat quality when defrosted, not to mention that it could take many days for the interior to freeze solid (which could also impact quality).

And "freezer burn," by the way, isn't necessarily caused by long storage: it's the result of poor packing, usually combined with temperature cycling in a freezer, which allows air near the surface of food to lead to oxidation and dehydration. Yes, a poorly packaged food will get worse over time, but a properly packaged food will last years in the freezer with no freezer burn. (For a whole hog, you'll need a large chest freezer at home, preferably one without an auto-defrost cycle.)

Anyhow, my personal recommendation would be to seek out a local meat packer or meat processor with access to a commercial freezer. (Perhaps there's someone who people take game meat to for processing or something?) Ask them if they'd be willing to freeze the carcass after slaughter and vacuum seal it for you. The vacuum sealing will significantly help to prevent freezer burn. I don't know whether vacuum packing is feasible depending on how large the pig is (many processors only do it with small whole pigs), but that would be your best bet.

They'd also be able to advise you on the feasibility of freezing a larger pig for that long if they can't vacuum seal it. But my guess is that it should be fine for a few months if you can keep it consistently below 0F and away from temperature cycling.