Herpes transmits between people very easily, which is one of the reasons it's such a common disease. Although people think of herpes as an STD, it can also be spread through more casual skin-to-skin contact, such as during wrestling. This type of herpes is referred to as mat herpes or, more correctly, herpes gladiatorum. It is most often caused by HSV-1 - the virus that usually causes oral herpes.
Herpes gladiatorum is thought to be spread primarily by skin-to-skin contact between wrestlers, not through contact with the mat. It is usually found on the heads, necks, and faces of wrestlers, although it can also be found on the arms and hands, and there are guidelines available to athletic officials to reduce its spread.
There is very little recent data about the transmission of the herpes virus from objects, instead of from person to person; however, studies in the 1980s found that the virus could survive for several hours on plastic surfaces in a humid environment. This suggests that herpes transmission from infected exercise equipment is possible, even if the mat is not the most common source of mat herpes.
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Drugge, JM and Jackson-Allen P. (2008) "A Nurse Practitioner's Guide To the Management of Herpes Simpiex Virus-1 in Chiidren" Dermatology Nursing 20(6)455-66
Nerurkar LS, West F, May M, Madden DL, Sever JL. (1983) "Survival of herpes simplex virus in water specimens collected from hot tubs in spa facilities and on plastic surfaces." JAMA. 250(22):3081-3.