Unless she is lame and can't walk, it is not an emergency. She lived 13 years without being trimmed; She is not going to die from it now.
I have big, soft cotton rope 25 feet long. I pick up feet with it on anything I want to teach to be good about their feet.
To pick up a front foot, I tie the end of the rope around the horse's pastern, put the rope up over the horse's back the pull the foot up from the other side. Really big, stout horses may need you to stand on the same side, put the rope over its back and then under its belly back to you.
I usually do this tied solid and also use the soft rope to 'sack them out'. I would not do that with this mare until her foal is weaned. If she is heavy in foal, you can put her in a BIG stall or pen with a corner. Put her nose in the corner to pick up front feet and put her butt in the corner to pick up the back feet. It will take two people; one to hold her and one to work the rope. I used to do that with visiting broodmares and never put them or their pregnancy in danger. Since you don't know much about her, you do not want to set off a big fight.
You will not have taught her anything but to fight harder if she gets the foot down before she relaxes and stops fighting. But, the instant she does quit fighting, let her have it back. After the first time that you release it at the right time, it will keep getting easier and you keep it up longer, little by little.