Oh, I thought you would know! Cowboys across America started taking rubber from an old innertube and wrapping strips around the horns on their saddles, years and years ago. This gives their ropes (lariets) grip just like rodeo cowboys and team ropers.

However this practice is severely frowned upon in buckaroo circles in Northern Califonia, Oregon, Nevada and Southern Idaho. These places hold to the original Spanish tradition of doing things and would never put rubber on their saddle horns. To do so would be a disgrace. Many times I have seen and heard a "buckaroo boss" tell some new guy, who is about to throw his saddle on a horse, "Before you ride for this outfit you had better cut the rubber of that horn". I even worked for a guy that made us all cut our back cinchas off too. Our horns are wrapped with "mule hide", it is really just crome tanned and split cowhide. It is white or grey, perhaps it is on your saddle in the photo, it is hard to see. Since it looks like you are carrying what looks to be a short, braided rawhide reata it should be safe to assume that you do not have a rubber wrapped horn. If you did, that reata would probably break the first time you roped a cow with it.
Anyway I am glad to see that you have the good sense and judgement to be a cowgirl! And a very pretty one too, I might add!