I know of at least one man off hand, who would meet today's standard of Dwarfism.

His name was Vernon "Shorty" Keogh, an American Pilot who flew for the French during the battle for France and for the Royal Air Force during the Battle of Britain. He was also one of the first member of The Eagles, A squadron in the royal Air force that was established so American Pilots could fight for England without breaking America's Neutrality laws.

Now he was listed of having a height of 4'10" and according to mayocloinic that means Vernon was a dwarf ( it is entirely possible though, that in 1940 the defintion of a dwarf was different). Although, his fellow pilots always believed he added an inch or two to raise the possibility of him being accepted into service. He had to sit on two cushions just so he could see out of the cockpit in his spitfire and he had to personally modify his pedals to accommodate his shorter legs.

My main source is The Few, by Alex Kershaw.

It's a great read if you are into Arial Combat or just WWII in general. It follows several RAF and Luftwaffe Squadrons during the struggle for Air Superiority during the summer of 1940

Here is a picture of Vernon(center) with fellow Americans Eugene Tobin(left) and Andy Mamedoff(right). They're getting their Eagle Patches(Eagle Squadron).

Edit: added picture

A 1919 report on Defects Found in Drafted Men looked at the reasons draftees were rejected from U.S. service. One of the conditions for rejection was "defective physical development," which even the authors of the report call a "somewhat vague term." This could be on account of not meeting height (61-78 in), weight (118-211 lbs), or chest measurement (31-38.5 in) requirements. This could also be a failure to meet the more nebulous requirement to be "well developed and muscular" as well as the general requirement of meeting "special ideals of physical fitness corresponding to the special service he has to perform."

The report found 8004 men were reported as underheight, of which 7694 were rejected. The remainder were divided roughly equally into general and limited service. There was some allowances made to physical requirements, but it seems exceedingly unlikely that someone with dwarfism would have been accepted. By modern definition, the condition would put them a couple inches under the minimum and the most common form of dwarfism, achondroplasia, is typified by foreshortened limbs relative to the body. If the height requirements did not immediately exclude them, in other words, the more vaguely defined standards might (and there were also performance requirements as well, like marching with heavy packs and such).

As an amusing historical side note, the authors of the report cite a key reason so many men were rejected for "defective physical development" (most of whom were underweight) was:

due to recent immigration into this country of representatives of races of southeastern Europe, many of whom of normal constitution are below the lower limit of stature and weight prescribed in the prewar standards of physical examination.

It should also be noted that one of the authors, Charles Davenport, was very big into eugenics.

There were anthropometric studies carried out at the end of WWII as well, such as Newman and White (1946) Reference anthropometry of Army men. The current U.S. Army standard for height are 60-80 in, though, so this should give an indication of how little the requirements have moved. This isn't just a simple factor of discrimination, but also has to do with the standardization of mass producing military equipment even for recruits and draftees not in combat roles, hence both upper and lower bounds on the requirements.