AMHA:
Rule GR-045 RING PROCEDURE
A. Dress: It is the tradition of the show ring that all handlers and
drivers be correctly attired for the classes. Hats, boots, gloves,
and long sleeved shirts/blouses or jackets are REQUIRED in
all SHOWMANSHIP classes only. Failure to do so will result in
disqualification in that class. Management and or officials must bar
any entry or person from entering the ring if not suitably attired to
appear before an audience. No farm, individual, or horse names or
farm logo may be displayed on exhibitor, horse or vehicle, except
multiple hitch, draft harness classes. In halter classes, hats, boots,
and gloves are optional.
AMHR:
1.4 Ring Procedure
A. Dress: It is the tradition of the show ring that handlers
and drivers be correctly attired for their classes. Tshirts,
shorts, clothes with logos or monograms are
not correct attire and will not be allowed in the show
ring. Horse and handler must look their best. No farm, individual or horses names may be displayed on exhibitor.
So, yes, you need to cover it up.