How old is that tire? Has the rubber hardened?

If it were me, I would want new rubber on, especially in front. A flat for whatever reason on a mountain descent isn't my idea of a good day. If it is preventable, I do what it takes. An old fashioned beaded tire or solidly glued sew-up have better chances of staying on the rim until you stop than a folding tire.

You may hear otherwise from others, but I would change that tire just for peace of mind.

Ben