A-HA! This mystery is now solved!
See, Ice Cream Dolls were only manufactured with cloth bodies, but hard-bodied ones were sold as crafters' bases. I thought for a long time that this was a crafters' base doll with clothes somebody sewed on, but the OP said that he came that way. Then, today, I discovered this:
Tada! So as you see, he is actually a "Rainbow Kids" doll, not a true Ice Cream Doll after all.