That was put very nicely, I was thinking something similar ...she might not be happy with you feeding her horse as well, but if you introduce yourself first and express how much you like her horse etc.Please get some lessons under your belt first!! And go over and introduce yourself to your neighbor! You could offer to help her with horse chores to gain some experience with working around horses. Also, (I have been sitting here trying to figure out how to say this tactfully, but if it is too blunt please forgive me) I have had people approach me, that I don't know wanting to ride my horses. It really has taken be aback! I think that a better approach would be to introduce yourself, explain that you love horses and what your plan is (taking lessons etc). She may offer. If she has more than one she may like the company of another person on a trial ride. Good luck!!!
Hopefully she understands you only mean well and loves the offer for help.