The existing old finish may well be shellac. Lots of it has been used over the decades for exterior projects because lots of folks don't know any better. To determine if it's shellac, wet an area on the upper portion of the door with some denatured alcohol and keep it wet for a minute or so. Then try rubbing the finish off with a clothor a piece of #000 or #0000 steel wool. If it comes off, it's almost certainly shellac. You can then strip the rest of the door this way also.

If it doesn't come off with the alcohol, thenit's most likely an oil-based varnish. All oil-based finishes amber with the passage of time.

Most woods will turn gray in color when unfinished and exposed to these types of weather extremes. Sand deep enough and you'll likely find wood cells that aren't as fried. However, if this door has been left without finish for a long time...you would likely have to sand quite deeply and that isn't really practical.

From what you describe, I would likely resign myself to coloring the entire door the same dark color (or darker) than the lower portions turn when finish is applied. This will entail stripping the entire door first, of course. If you don't the wood won't be able to absorb the stain.

Once stained, apply a couple/few coats of a quality exterior spar or marine grade varnish.

Or...there always paint.

Or....you could add some dark trans-tint dyes to your exterior varnish.
http://www.homesteadfinishing.com/htdocs/TransTint.htm

Note the specific instructions for adding these dyes to oil-based finishes.

Frankly, I would not put the effort or money into applying a colored varnish over doors that are bearing old finish and really need more attention. In doing so you would make stripping them in the future all that more difficult and expensive.

If you don't think these doors are worth the effort of doing the job right because they aren't going to survive for long anyway...I would suggest sanding them enough to remove any flaking finish and then paint them. Quicker, faster and cheaper. (Prime the bare wood areas first before painting, of course)