What’s coldest Month in Denver Colorado?

The winter temps in Denver can be below zero.  The coldest month is usually January, but any of December, January, February can get pretty cold.

Denver is along the edge of the mountains, an area known as the Front Range.  The Front Range runs parallel to the foothills for the Rocky Mountains - more or less follows I25.  The weather along the Front Range is usually very different than what the weather is like 20 miles to the west up at 10K' elevation.  It can be zero degrees and snowing along the Front Range one day and sunny and 60 degrees the next. 

Colorado has very low humidity, so even though it's cold it won't feel as cold as the same temperature would feel in an eastern US location.  Having lived in Colorado and New England I prefer the Colorado winters.

You will adapt to the climate in the course of a couple of years, the weather shouldn't be a reason not to move there.  I'd be more worried about what you will do for a source of income.

On average, December is the coldest month here with an average high of almost 43°Fand an average low of 17°F, but it can vary a lot from day to day.

http://www.rssweather.com/climate/Colorado/Denver/ says it is January

Why not ask your family instead of a bunch of strangers on the internet?