Hats Are In A Continuity Error
This is a simple continuity error, something regular movies have a lot of (for good reason). It is pretty hard to keep track of where everything is in each scene. But in an animated movie, it’s a little weirder.
When Roger is out walking Pongo, on the beautiful day they will both fall in love, we see him leave his hat on a bench.
Then, when Pongo suddenly takes off in his quest to go meet the Dalmatian lady he has spotted with his nose, the hat is back. It’s clearly on Roger’s head when him and Anita are awkwardly tangled up in their dogs’ leashes.