Ryle pretty much covered it. I would especially be careful not to share feed or water buckets, or grooming tools. BRING YOUR OWN, even if the show grounds supplies buckets. If you use a stall there, you might consider spraying it down with a 50% Bleach solution (on the walls, door, windows, bars, dirt/ground, mats, etc.) to kill any nasties that are there. Bring your own shavings or buy pre-bagged shavings.
Supplements won't really help much. The only supplement I would consider would maybe be an overall vitamin supplement, just to make sure you have all of your bases covered. If you're feeding more than half the recommended levels of fortified feed for your mare's weight and activity level, I'd go with 1/2 the recommended dose of any of the following supplements: SmartShow - Multi-Purpose Supplements from SmartPak Equine Winner's Daily from SmartPak Equine Grand Vite from SmartPak Equine Accel - Multi-Vitamin Supplements from SmartPak Equine
If you're feeding half the recommended levels of feed or less, or no fortified feeds (whole grains or no grains), then I'd feed a full dose of the above, or a full dose of any of the following: Accel Lifetime from SmartPak Equine Select II from SmartPak Equine SmartVite Maintenance Grass from SmartPak Equine Mega-Cell? From SmartPak Equine
If you're feeding a ration balancer, other than Purina, then you shouldn't need any extra vitamins. If you're feeding Purina Enrich, then I might consider supplementing with extra vitamins, at the 1/2 dose.
Dose that many any sense? Lol