Because the effect of the haze gets stronger as objects get more distant, it really adds depth to an image, as long as you have nearby objects which are less affected, midrange objects and distant objects. The further objects will get more and more faded.

This can work to your advantage if you can find situations where there are a series of mountains further and further away, you can get very nice images where the closer mountains are less hazy and the rest slowly fade out. Like this shot, taken before sunrise:

Or if all of the background is the same distance, and will be equally hazy, you need to find something else for foreground interest. Could simply be a tree or rock. Anything that isn't "hazy" to instruct the eye that the image isn't simply washed out, but that the background must be very distant due to its being so faded compared to your foreground.

Because haze reduces contrast, in post processing, you ought to be able to fix the images to a degree by bring down the blacks and boosting overall contrast (using curves) or midtone contrast (using clarity slider or equivalent in whatever editing program you use).

As well as lowering contrast, the haze desaturates the colours, so you may want to boost saturation or vibrance.

Here is a quick edit - in RAW converter

• +50 Clarity
• +20 Whites
• -20 Blacks
• +10 Saturation

Then in Photoshop added a warming filter to the land areas, and various curves layers to the sky, water and mountains.