Any way they could. In the Ninteenth century, beer wasn't drunk as cold as today, the English and Chinese still drink pints of ale warm, but the cowboys prefer it cool.
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In colder areas of the Western US, saloons gathered ice from frozen lakes. The ice was stored in ice houses where large blocks of it were insulated with sawdust, keeping it frozen for months.
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Even where it wasn't cold enough to freeze, a lot of saloons had access to a cool mountain stream, where they'd get cool water from a cistern to cool the barrels. What if there was no stream? Well, until 1880, most saloons had a root cellar, usually built into the side of a hill and stored beer under 50 degrees farenheit.
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What if you wanted cool beer at home? Most of the time, people ordered it take-out, in buckets or whatever, sometimes children brought it home, about the same as any fast food nowadays.
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Anyways, it sort of cooled itself naturally by having some of the alcohol evaporate. Also, it doesn't have to be cold, as there was no carbonation. Today, you need it cold to hide the taste of carbon dioxide.
--facts taken from Do Penguins Have Knees? by David Feldman, of Imponderables fame
Seems some people have taken umbrage at what I said. The British don't drink it warm, more like cellar cool, around 50 degrees farenheit. | 
