No you shouldn't really need any equipment, solid boots/shoes, even ponies hurt if they stand on your toes, if you want to be involved, I suggest making yourself available to lead, won't take you long to get the hang of it, general fitness a bonus :-) gloves come in handy then, as for competing...
I often wonder about the lady whose husband left her weeks before their baby was due, she had horses, a toddler and a brand new baby & a relationship fall out, I admired her strength. I would love to hear she is happy and life is calm again for her ?