During the winter I feed my mare (26 year old) free choice grass hay (which she hardly ever touched, except for when it was really cold) and about 15 pounds of alfalfa a day. I also fed her about 2 pounds of soaked beet pulp.
She's a pretty easy keeper (on grass it's hard keeping the weight off, on hay it's much easier) and that diet kept her chubby all winter.
I would definitely get your mare on a diet of free choice grass hay (basically, as much as she can eat, she should never be without food) and slowly work your way up to 10 or more pounds of alfalfa. If getting that much hay is difficult (I know some places are experiencing a severe hay shortage) I'd introduce soaked alfalfa pellets and beet pulp to her diet. In any case, it would probably be beneficial to start her on soaked pellets because at her age, it's possible that her teeth aren't really in working order anymore. Speaking of which, have her teeth been checked by a vet?
Basically, if you can get it so that she's basically swimming in food (work up to that much gradually though!) that she can digest easily, I'll bet you'll see a marked difference in a month or two. Over the summer I was working with a horse that started out looking like she did in the first picture and once I got him on 20 pounds of alfalfa and ten of grass everyday, his weight got up to almost normal in about a month and a half. After he gained the weight he was able to easily keep it on with just 5 pounds of alfalfa a day and 15 of grass (and no work, he would have needed more had he been working). It was just a matter of getting him there.
If it were me, I'd go for that alfalfa. That's a good price and it more than likely will only do good things for her.
Good luck! She's lucky to have someone like you who wants to see her fat and happy and isn't using the "well, she's old" excuse. :) Age is no excuse, unless there is a severe underlying condition.
Fabio - 13 year old Arab/QH gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.