Scarves for winter need to be soft and cuddly to keep you warm however summer scarves need to be open and absorbent so that they don’t make you hot. Good fibres for summer include cotton, linen and silk. Fine weight wool and alpaca are ok too as long as the scarf isn’t too thick.
For summer I prefer woven scarves, they don’t hold heat in as well as knitted fabrics (as shown in year 5 science experiments) so they work better for summer especially when woven loosely so there is a lot of air.
Weaving linen is difficult as it is inelastic and difficult to keep even. That means that the result is quite rustic and nothing like a machine made fabric especially at the linen is slubby. Hand made fabrics will never be uniform. Its one of the things I like about handmade.
So now I have my pink silk/alpaca scarf, my blue silk/cotton scarf and my new green linen scarf. That is a good selection for summer when added to my knitted lace summer scarves.