The main character is a man in his 30s(?) who makes a living doing odd jobs. He is frequently transported to a fantasy setting world where he inadvertently helps the people he meets, before being transferred back to where he was just before the shift to the fantasy world. He doesn't realize he is being transported to another world for a few chapters and does things like play with a giant cat monster, and sell a man with weak ice magic a shaved ice.
Could this be Part Time Overworlder?
Meet Tanaka. He’s a 26-year-old freeter - a guy who makes his living on various part-time jobs. He works in warehouses, directs traffic, and generally does whatever work he can find in order to get paid.
However, recently Tanaka has had a problem. He occasionally is transported into another world, usually in front of people who need help. Knowing nothing, can Tanaka add another part-time job to his repertoire?
The shaved ice magic situation is about three chapters in.
Found with a search for
isekai manga unaware "shaved ice"