As noted above, water content within the air is the dominant effect. Colder air holds less water, so in general, winter atmospheres have less water and are more transparent.

The variable usually used to capture this (i.e., modeling the effect of water on atmospheric clarity) is water column content, measured in grams per square centimeter. This is the mass of water in a column of atmosphere 1cm by 1cm, from the Earth surface up to the top of atmosphere. It typically ranges from 0 to 5 g/cm2, at least for non-cloudy atmospheres.

At 5 g/cm2, your naked eye will notice haze and muted colors. The colors are muted because some spectrally distinct light from distant objects is being intercepted by water and scattered as white light. E.g., a fraction of the greenish light reflected from a tree is absorbed by water and re-radiated as panchromatic light, before finally reaching your eye. So you see 90% photons from the tree, and 10% photons scattered off water between your eye and the tree. And of course this scattering causes blurred edges as well.

This variable (column water content) can be measured by scientific instruments in several ways, fairly directly, by its impact on the spectrum of sunlight. NASA has several satellites that make this measurement regularly, sometimes just to calibrate out the effect of atmospheric water on other measurements.

Here’s a nice map of water content, animated monthly: https://earthobservatory.nasa.gov/global-maps/MYDAL2_M_SKY_WV

You can see the decease in atmospheric water in Colorado in the winter months, when the atmosphere there is dominated by cool, arctic air; and then increasing in summer as you get air from the tropics. (As the narrative explains.)

You can also notice stronger seasonal effects over land than over oceans, partly due to thermal regulation by the ocean’s water mass. Again, this makes mid-Continent areas like Colorado have a stronger seasonal “swing” than, say, coastal California.