"To go out on January day and run around on the beach under a golden sun makes a very great change in your outlook on the universe."
- Robert Silverberg

The suit was also heated, and had its own supply of air, when disconnected from the spacecraft itself:

Provision had been made to meet the terrific cold which we knew would be encountered the moment we had passed beyond the atmosphere—that awful absolute zero which men had measured by anticipation, but never yet experienced—by a simple system of producing within the air-tight suits a temperature sufficiently elevated to counteract the effects of the frigidity without. By means of long, flexible tubes, air could be continually supplied to the wearers of the suits, and by an ingenious contrivance a store of compressed air sufficient to last for several hours was provided for each suit, so that in case of necessity the wearer could throw off the tubes connecting him with the air tanks in the car...

Just a few years later, the 1902 French movie La Voyage Dans La Lune depicted men walking on the moon in top hats. (Thanks to Jim Sharkey for pointing that out.)

The vacuum of space was still being explained in 1929, as in The War of the Planets by Harl Vincent:

“But,” interrupted the Secretary, “how were you able to pass from one vessel to the other when both were in the vacuum of outer space?”

“I was enclosed in an air-tight suit with an oxygen supply system as was the observer on the deck of the enemy ship,” the professor replied...