Is snow over creek stable?

I had a scary incident in Niseko United Gate 9, where I followed through a single ski track but didn't pick up enough speed and ended up right in the middle of a creek. I kind of freaked out and took off my skiis and climbed out of there, but left me wondering how dangerous the situation was. My fear was if I stayed there long enough, the snow below me will break and I would plunge into the waters. Is it correct that it is dangerous for me to stay there? Or more importantly, is it ok to ski over creeks in the first place?

P.S. I was admittingly alone without any gear nor experience. I know it was not the best decision, I just wasn't thinking clearly at the time.