I am new to this, so please bear with me. I just got my three horses three weeks ago. I do not know anything about my older horses before I got them. About a week ago I noticed that Babs (my 20+ paint mare) started walking very stiff. It even appears sometimes that she is on the verge of tripping. A friend of mine said to give it a couple of more weeks because it may be due to change in diet.

I am really concerned about her. Any suggestions?

Hopefully it is just old age.
If you've gone from a flat field to hilly, that may be your culprit.
Any joint supplement is always an idea. That really is trial an error to see which one works best for each horse.
Or it could be something more serios, such as;
Lymes
EPM
West Nile
EHV
Wobbler-although that isn't age related
A blood count is really a good starting point, for a medical cause.

Would that be covered under the coggins? I know they had this done as they were bought at a public sale.

When you handle her legs do they seem stiff and creaky?

Of all of the things on Ltc4h listed, none are related to a Coggins. Coggins is the "name" of a test.

It is used to test the sickness E.I.A. (Equine Infectious Anemia) which is a rare disease in horses and now is about unheard of in my state. It is spread by flies which makes the Coggins Testing basically usless (yes fairly much a scam for money, to be blunt) because at any given time, even seconds after your vet draws blood from your horse to check for the disease, an infected fly can come up and bite your horse, giving it the infection. So no matter if she has a shiny brand new coggins test done, or if it is months old, still will not tell you whether or not she has EIA or not at this specific time. But not to worry, during cold months there are not flies so it's not spreading, it is also fairly rare.

Sounds to me like old age, possibly cold weather bothering her joints? Try a joint supplement, such as Glucosamine or MSM (MSM is an anti inflammitory and I can guarantee it to work on stiff joints, I also have a 70+ yr old friend who uses it for himself), but if you want to be extra safe, have your vet check her, or at least give him/her a call. They may have some suggestions for you.

Hope that helps