I'm sorry, I had misunderstood your original post and was under the impression your mare was only bred (possibly) three weeks ago.
But I'd still back your vet at this point. If your mare is 10 months along, as CheyAut said it would be very difficult for your vet to "miss" the baby on a palpitation. It's a good idea to be prepared in any case, of course, have the supplies you need and keep your vet on call. But I'd trust your vet's greater wisdom at this point, if he says no baby, assume there is no baby. As I mentioned in a previous post, if you are concerned he might be wrong, ask him to do an ultrasound.