I have the tail of every horse I have lost. I braid the tail, rubberband it at the top and bottom of the braid then cut the braid off just below the bone before I put them to sleep. I keep all the tails in separate ziplock bags with names and dates written on the bags along with a photo of the horse. Some day I would like to make fly wisps out of the tails to hang in my equestrian room in my house. I also have lamp made out of the shoes of my Clydesdale "Seamus".
I have the towel that my Dalmation, 'Dottie" slept on also wrapped in a ziplock, I keep it in the linnen closet, top shelf. About once a year, when I clean the closet, I open the zip lock take a big whiff and have myself a good cry. How I loved that dog, and it has been 15 years, her smell is still strong.
So do I think it is weird that you want to heep your horses scent... not at all!!