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The noun ice-cream van designates a commercial vehicle from which ice cream is sold, typically at the roadside.

This noun occurs, for example, in the following paragraph from The Talented Mr Ripple, about Mr Ripple, a Dublin ice-cream man, by Conor Creighton, published in the Evening Herald (Dublin, County Dublin, Ireland) of Friday 20^th June 2008 [page 32, column 1]:

There’s nothing sadder than the sight of an ice-cream van entering an estate, jingle playing, lights on, turning once, turning twice and pulling to a halt only for no kids to bother coming out of their homes. It’s like Big Ben without the chimes, the Eiffel Tower without the illuminations or Katie Price without the boobs—it’s just not right. Children are an ice-cream van’s lifeblood.

These are, in chronological order, the earliest occurrences of the noun ice-cream van that I have found:
—Note: These early occurrences indicate that, originally, at least in Britain, ice-cream vans were typically at fairs, i.e., at periodical gatherings for, or incorporating, entertainment, at which rides, sideshows and other amusements are set up:

1-: From The Sun (New York City, New York, USA) of Friday 29^th May 1874 [page 1, column 2]:

Tomasi Tosano, an Italian, of 69 Baxter street, sells ice cream at First avenue and Ninth street. A primary school is near by and Tosano has been very much troubled by the pranks of the children, who throw stones at him and throw sticks into his ice cream. At the noon recess on Tuesday the children as usual crowded around his ice cream van and so worried the Italian that he seized Robert Platt, aged 5, of 309 East Ninth street, and threw him violently to the ground.

2-: From the Fort Scott Daily Monitor (Fort Scott, Kansas, USA) of Thursday 11^th June 1874 [page 4, column 2]:

The chap who engineers Cretor’s ice cream van, as he passed along the streets last night, lustily yelled, “I scream.” We should say he did.

3-: From an account of Newton Abbot’s annual fair, held on Wednesday 22^nd September 1875—account published in the East & South Devon Advertiser (Newton Abbot, Devon, England) of Saturday 18^th September 1875 [page 5, column 6]—in this text, mustle is either a variant or a misspelling of the noun mussel:

On entering the market from Queen-st, nearly the first thing you came to was a “quack” palming off his shilling bottles of stuff to “rub-in” and cure everything. Then you came to the cockle, and mustle stalls and ice cream “vans” which were well patronized.

4-: From the following advertisement, published in the Evening News (Portsmouth, Hampshire, England) of Wednesday 14^th January 1880 [page 4, column 2]:

NOTICE.—Mr. Antonio Tiscornia, 13, Meadow-street, Landport, intending moving from the town, has for Sale four hand Ice Cream Carts, complete with the necessary apparatus. Also, Pony and Ice Cream Van complete.

5-: From Local Notes, published in The St. Helens Examiner. And Prescot Weekly News (St Helens, Lancashire, England) of Saturday 30^th April 1881 [page 5, column 1]:

Another April “fair time” has been and gone, and the event is numbered in the chronicles of the past. As usual the fair ground has been invaded by itinerant showmen, proprietors of hot pea saloons, stomach testers, weighing machines, and ice-cream vans; manufacturers of toffy and coloured waters; perambulating vendors of nuts and gingerbread, tripe and trotters, hot pies and questionable looking ham-sandwiches; owners of hobby-horses, swing-boats, dolls, shooting-galleries, and the thousand and one varieties of oddities and commodities to be found in an extensive fair.

6-: From the Leicester Chronicle and The Leicester Mercury (Leicester, Leicestershire, England) of Saturday 11^th August 1883 [Supplement, page 3, column 2]—in this text, the noun highflier designates a swing used for amusement at fairs:

NORTH LEICESTER FLORAL AND HORTICULTURAL SOCIETY.

The increasingly popular exhibition under the auspices of the above society was held on Bank Holiday, as in former years, with every fortunate circumstance tending to its success. The weather, yesterday, although threatening at times, was of such a propitious character as to render outdoor amusements thoroughly enjoyable, and the thousands of persons who congregated on the field set apart for exhibition purposes were not oly [sic] attracted thither by the fine display of flowers, fruits and vegetables, but also to witness the excellent amusements, in the shape of aquatic polo matches, &c, provided for their delectation. […] Other parts of the field were covered with “highfliers,” ice-cream vans, roundabouts, and the usual concomitants of fete and gala, while in a separate corner Professor Carre had a tent erected wherein to prepare his firework apparatus, and the fancy fire balloons, which, at intervals during the afternoon, he despatched on their ærial flights.

7-: From Harrow Green & Wanstead Slip, published in the Eastern Mercury (London, England) of Tuesday 18^th June 1889 [page 8, column 4]:

All Among the Ice Cream.—On Friday morning last, the tramway in Leytonstone-road near the Thatched House was obstructed for nearly an hour by the collapse of an ice cream van, in consequence of one of the wheels breaking.