A Mamoswine is now available to obtain from the Pokemon Global Link if you've got an account. More importantly, Swinub hasn't yet been released in the Dream World IIRC, so this will be your only chance to get a Thick Fat Mamoswine for quite some time. The password for it is POKEMONDOTCOM (yes, written as DOT and not an actual period).
Thick Fat really is a great ability too, especially for Mamoswine. Mamoswine is immune to electric and resistant to poison; that's all it's typing gives it. Giving Mamoswine an Ice resistance and neutrality to it's Fire weakness really helps this gargantuan switch in safely and abuse it's huge attack stat and STAB Earthquake. This is especially true if you're using Mamoswine outside of a Hail team, since Snow Cloak would be 99% useless to you (and Oblivious is always useless ). Thick Fat is basically this glass cannon's padding to help keep it from exploding after it gets off an EQ, so yeah. Get it while it's... uh, cold.