I don't live there, but there's a Las Vegas board here on the DIS - under the DisneyLand section - and a couple of the posters who offer advice there DO live in Las Vegas.
But when I visit in late December, it's usually in the fifties during the day and the thirties at night. Two years ago, it snowed in the city (as opposed to the normal mountain snow) December 17!!!
It's cold by Vegas standards. Here are the averages: January 58° F (14° C) 34° F (1° C). But it's not too bad. It gets a bit windy but we don't usually get much rain.
The first day was GORGEOUS in the 70s...the second day was 60s and VERY windy--downright chilly. Major resorts have pools open all year, but be sure to call & ask wherever he is staying.
I was there Jan 23rd last year. The days were fine, cool, but sunny and nice. Evenings however, walking down the strip at night, VERY chilly! We wore down jackets and gloves and were chilled.