IPhone froze on apple logo screen can I just take SIM card out?

Okay so my iPhone 5s froze about 2 days ago and i tried to reset it to no avail. Then I took it to a phone place and they couldn t get it to work and my phone has no storage so I'm thinking of just buying a new phone and switching out the SIM card with my old one. Is that possible if I was to get an iPhone 6 or iPhone 5s but with more storage? Or would the freezing of my phone possibly be an issue on the SIM card as well thank you for answers

Has nothing to do with a SIM card.