Here’s a fascinating article about “official” clothing for the (still existing) Cyclists’ Touring Club of the UK from back in 1890! Yes, tweed abounds as they found it a very practical cycling outfit!
Note what they had to say about wool: “This was settled on ‘after many months of patient investigation’ and testing of over forty different cloths. At the time wool was favoured against the skin, as a hygienic and sanitary fabric, far better than cotton for the rigors of riding. Dr.Gustav Jaeger was partly responsible for this, with his ‘Sanitary Woolen System’ which was popularised by the Royal Family, amongst many other patrons. So, woolen undergarments were also specified.”