Burl Ives is the one you are talking about for Holiday memories for me. He's associated with the voices of the narrators for the claymation Christmas cartoons (Rudolf, Frosty, The Year Christmas Almost Wasn't etc).
He never did the Parade that I know of. Famous past hosts of the parade are Lorne Greene, Betty White, Bryant Gumbel, Mary Hart, Sandy Duncan, Deborah Norville, Katie Couric, Al Roker, Willard Scott. The only ones from that list of past hosts that would be "portly" were Lorne Greene, Al Roker (he's lost weight now) and Willard Scott. None of them were by a fire as it is a live commentary event and no fire outside.
Are you sure the parade you are thinking of is the Macy's Thanksgiving parade and not the Rose Bowl (New Years Day)? It would be much colder then and in need of a fire and a lot more stars guest host that one. One of the most notable would be Ernest Borgnine.