Cross-country skiers can probably be supported by ice that's something like two inches thick if the two inches is high quality ice as opposed to mushy ice. The skis distribute the weight but you got to move along smoothly without slapping the ice or pressing it with a ski pole.
It all goes great until you break through to the other side!
Did you know that a swimmer's noodle makes an excellent waist belt, ice safety pfd-style belt by wearing it as a waist belt with a rope threaded through the center hole and you can wear it under your coat, unseen, so's you don't look like a dweeb. ....
Like no kidding ....... you didn't know that ..... did you! ..... a foam noodle belt will support you in icy cold water and make it easier to crawl back up and onto the ice shelf ...... or something! .....
..... It will also ride up to under your arm pits and support a deceased frozen dead body after succumbing to the 34-degree cold water. Your hands can freeze up in like ten minutes, leaving them useless to use, but it can take 60-75 minutes to actually die from cold water immersion so it helps to wear a noodle belt, carry self rescue spikes and a whistle.