My mom's been wonderiing if it is normal for for a parrot to climb up ladders & things foot over foot. Like how we humans climb stairs & such. Winkie does it all the time.

Not usual but not uncommon either. They usually use their beak as well.

Yes, Winkie does use his beak quite a bit especially when he's climbing on my shirt. (Sometimes even more than big parrots - I think.)
Thank you.