Short answer: Yes, Do it.
A lot of folks have the impression that Aquarium Plants need Tropical Tank temperatures to live. This is just not true. Oh, sure, some do but the wider majority do not.
You may have seen my tank in the gallery[here]. It looks for all the world to be a tropical fish tank. It is, however, a pleasant chill at 67-68 degrees F.
You can find lists online of TEMPERATE aquarium plants to choose from but I have a few favorites...
Pretty much any Anubias! The fact is you can even acclimate anubias to live well in SALT water. They are about as hardy as it gets folks! Just remember not to bury their roots (they will rot and the plant will die).
Java Ferns are another plant that looks great and does well. I use the darker and frillier variety (forgot the name, sorry) but if you look under Java fern in Google Images you will be purely in awe of how many types and all the ways they can be used!
Like Anubias, you cannot bury the roots in soil. -- I should mention I have a soil substrate tank... Anubias and java ferns can certainly have their roots under gravel!
If you have a soil tank or want to pot and fertilize...
Hornwort and Eludea are excellent for a read planted screen. Cobomba is excellent if you want a more of a fairy-fern sort of thing...
My absolute favorites should already be obvious if you've ever kept or considered a pond; Lilies!
Tiger Lilys, Banana Plants and the like are beautiful and send up leaves to the surface where they get light... and they shade your Axolotls' lidless eyes!
Another favorite of mine is the dwarf red lotus. These grow exactly like the lilies but are, as noted, red. The leaves provide some nice contrast to the tank.
On the topic of light screen... how about adding water lettuce or a similar floating plant... maybe even riccia fluitans [Crystalwort]?
Pros:
Live plants add nutrient and trace elements to the water as well as O2 at night.
Your animals will likely enjoy laying about the leaves of your plants.
Cons:
You will have to account for the lower light and temperature... You should add a CO2 releasing plant supplement (Flourish Excel for example)
You WILL get some algae and the plants too will get it. Not much, the cold is not really algae friendly but know that it is going to happen. Frankly, it looks normal and a little maint once a week and a once over on the glass with a scraper once a month will more than take care of it.
Not exactly a Con but you should also not expect the plants to grow as fast as they might in a tank with bright light and a CO2 rig. So don't be afraid to get larger specimens when you buy them.