Have you tried reading time for toddlers at your local library? I see a lot of moms talking to each other there as little ones are listening to the librarian read them a story or if they watch a little puppet show. You can meet some other mom’s there, some may even be single moms as well. I think you said you were a single mom, if not please forgive me.
Also you said horseriding is an interest of yours.
Does the place you have your horse, offer riding lessons to kids? That is a great place, the barn, to meet other moms who have their kids taking lessons. You don’t have to be the teacher giving the lessons, just hang out around the barn. I know my daughter made friends with this single woman who had a beautiful horse. In fact, she knew most of the kids who took lessons at that barn because she was there so much. I knew her as well. So the barn is a great place to meet someone. As someone else said, be a friend and soon you will have friends.
Those are just two ideas I had from what you wrote. I hope it helps.