How suitable leather is will depend on how it is tanned, how it is treated, and what animal it comes from. The leather bar tape I tried years ago I did not like. It was slippery when wet, took forever to dry, and wasn't anything special comfort wise to start with.
Other leather bar tape may be much better, but I suspect that the average cow hide as it is usually tanned won't be great unless you figure out a treatment to use on it that enhances it's properties in wet conditions.
Personally I wear gloves pretty much any time I ride, but I find cork tape comfortable with or without gloves. Ditto for some of the synthetic tape, but they are more hit or miss.
As far as gloves go, I raced off road motorcycles and mountain bikes for years and had a pair of much prized deer skin gloves that I really loved. They were soft and stayed that way after much abuse even in wet muddy conditions. I never found another pair like them. They had no padding (other than hard rubber guard strips sewn on the backs of the hands) and were not intended as bicycle gloves, but I'd love to gave a pair of bicycle gloves made from that leather.
Most of my bike gloves seem to have the leather treated somehow for wet conditions and the nice ones all seem to cost a bundle.