Cowpony best of luck. I hope it turns out well for you. I understand your desire to have a foal of your own. I do think we can tend to be a little quick to squash anyone's desire to have their own foal. I think the main thing is to be educated going into that you could lose your mare and the baby, that you could have lots of monetary expense, etc. Your mare may be just fine after but what if she isn't? Are you okay with that?
Having said all that I do think your comparison with adopting a child is a bit naive. There are lots of kids needing homes but adopting them is not easy. Also they are rarely healthy newborns without any issues. Fact is it is much easier to go buy a healthy weanling or yearling horse than it is to adopt a healthy child. Its a completely different situation and of course we are talking human life, not an animal per se.
I do think because of the extreme amount of unwanted horses and dogs and cats, etc. right now is a bad time to breed unless you have a very specific purpose and goal. I think its great you plan to keep and love the baby no matter what. However you could provide a home to a lovely existing baby, get the exact color you want and still get to raise a baby from the start.
However sounds like you are wanting your own and there is nothing wrong with that, sounds like you are equipped to deal with the possibilities and issues and have the means to support another horse so best of luck and if and when you have a baby share the pics .......