Why not have a pony party that doesn't have any actual live animals? I did this with my boy when he was little. Super cheap, too.
Make pony bingo cards -- you can get images of different ponies and make the cards in MS word with a table. Little pieces of carrot for the markers? We used pennies one year -- big hit,the kids kept the pennies! Or little plastic ponies,kids keep the little ponies.
Pin the tail on the...pony!
Activity for kids as they arrive -- make gift bags by decorating with pony stickers, markers, glitter....
Have them make pony cookies -- you make the dough and either have them use pony cookie cutters, or make the cookies ahead of time and have the kids decorate them.
I've got a zillion other fun cheapo birthday activities for little kids, let me know if you want to hear more!
Dang, I missed my little guy! Now he's a big ol teenager!