Yes, it’s true. It has to do with they way their legs work. Here is one explanation…
“This is actually correct stating that a cow can be led upstairs but not down. The ankle and knee joints are mis-aligned for supporting the cows weight when traveling down stairs. Its not that they physically can’t, its just that it is a lot of trouble for them. Imagine walking upstairs normally, but then when you come back down the stairs you have to wear a pair of ballet shoes and walk down on your tiptoes and you also have to bend forward at the waist the whole way down. you not only feel unstable, but you also feel like you might fall forward. This is probably similar to how the cow feels when trying to walk down stairs. Therefore, the animal is going to resist because of the fear of falling. Also a cows brain has trouble determining just how large a drop each step actually is, and the animal doesn’t like uncertainty. That is why anti-cattle crossing lines work for keeping them contained.”
I found it here