I'm 4'11 and 90 pounds, and I occasionally ride our pony mare who is about that size for a quick tune up, no more than 20-25 minutes at a time. Being that you're 25 pounds heavier than I am though, I'm not quite sure how she'd take to it expecially since you'd likely have to do quite a bit of vigorous riding to get her kid broke. At the same time though, sending her to a trainer isnt really an option because it isnt often that you're going to find a trainer smaller or lighter than you are.
That being said, I think that if you do it slowly and carefully, and give her LOTS of time to bulk up in muscle and be conditioned (get her endurance up lunging w-t-c first slowly, then ride starting at 5-10 minutes walking, 20 minutes walking, 15 walking 5 trotting, etc) and you don't do more than necessary to get her broke when it comes to cantering (and wait until she's very fit) then it might be ok. If possible, breaking her english might work better as well so you arent adding another 20-30 pounds for a saddle. 145 pounds is DEFINITELY way too much for her. Thankfully she's a really hardy breed though and known for their ability to carry small adults. Still, before I actually tell you it would be 'ok' I would like to see a picture of her. If she has an exceptionally long back or has bad legs, I wouldnt risk it.
If it isnt absolutely necessary though, and you have another larger horse for them to ride, do that and just let her be the cart horse that she is ;)
Thank you, I'd thought about this alot. She is not in "peak" condition or anything, and we are still at the very beginning of just building muscle. She's been a "standing in a stall" pony with her previous owners. I've been walking her up and down hills, and she'll walk with a small saddle strapped to her. (no one on it of course, just for some weight), and pulling her cart and sled. That's where we've started. She hasn't had any endurance training, or other muscle building beyond that.
I had thought of over the course of the next 3-4 months, work her on the hills more, and keep her longing untill she's tired, and then walk it off. Just to get her ready for me to sit on her for a minute, and that's where we start there. Make sure that she is ok with just standing there with me. If after 4 months of muscle building, she's not ok with me sitting on her, then forget it, she'll stay with her cart. (we don't have any other horses at the moment) If she is ok with me, start out 2-3 steps at a time. (unless she tries to take off...) Untill she is ok with walking forward for several steps with me. Then, just go one step at a time from there. If she is showing signs of strugling, I'll not be on her!
I will try to get some good pictures of her, and get them up here. With me standing with her, and such.