Something about the headlights gave it away. In any case, I found another link that gives a clear definition to some of these walk-in delivery vans. Somewhere in this PDF link to Vintage Truck Magazine, there's an article on the Hudson Business Car, which is not an actual car at all.
http://vintagetruckmagazine.com/pdfs/VT13-5.pdf

Hmm, maybe this post should be transferred to the "Useful Links" section.

I think Ddey65 may be right, it does look a lot like the ones from Thunderbolt and Lightfoot:
http://www.imcdb.org/vehicle_7947-International-Harvester-Metro.html
Dirty Harry:
http://www.imcdb.org/vehicle_2145-International-Harvester-Metro.html
and Teen Wolf:
http://www.imcdb.org/vehicle_83012-International-Harvester-Metro.html

I was having no luck searching around for “Ice Cream Truck”. The closest things I could find were Grunman, AM General and Chevrolet P30 like at
http://www.icecreamtrucks.com/used_novelty.shtml, but they just didn’t look right. So I gave up, figuring someone else may be more knowledgeable. Looks like Ddey65 nailed it.

That looks like an International Harvester Metro with the grille removed.

Smashing Pumpkins - "Today" (Music Video, 1993)
Ice Cream Truck ****