No, a UV filter would not have helped. If you bump up the contrast in the photo, that would help bring out the colors. One issue appears to be that, as is typical in the southeast, you took a photo of a subject off in the distance on a hazy day, and there's a lot of haze between you and the hills you're shooting.
The majority of lenses used by digital cameras now have micro coatings the reduce the UV haze.
The lenses used on older film cameras did not have this technology and relied on UV filters to reduce UV haze. Many users still keep UV filters on to protect the front element of the lens. This may also be unnecessary since the many micro coatings help lenses resist scratching. One can also use an NC filter for this purpose. Also if you use any filter, only use very good quality filters. Poor quality filters cause any number of problems.
Another source of 'haze' can be light flare on the lens. This is caused by the glare of a light just off the FOV of the lens. Once can reduce this by the use of a lens hood. Placing a UV filter or NC filter and using a lens hood will not always prevent lens flare.
If you are reasonably competent with post processing the histogram for this shot is unlikely to occupy more than half what is available, because of the "flat" middle of the day lighting. Adjusting the shadow and highlight end points and maybe the mid point on the histogram should produce the sort of image you wanted.
Photography is a bit like archery. A technically better camera, lens or arrow may not hit the target as often as it could if the photographer or archer does not practice enough.
The UV filter shouldn't help at all, because the sensors are not very sensitive to UV light - so UV pretty much cannot possibly be causing your problem. I agree that the issue is entirely due to haze and flat lighting.
_____ Brian... a bicoastal Nikonian and Team Member
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