I've been looking at dairy cattle for the past few years to see if there is any pattern to what side they use. Beef cattle may be different for some reason, but dairy cattle in those parts have no discernible preference. I've concluded that it makes no difference.
Jim - Another transplanted Texan
Former KCBS CBJ
Large and Medium Big Green Eggs , Black 18.5" WSM, Blue Weber Performer - Stainless, Green Weber OTG Kettle , Brinkmann SnP Pro, and a Stainless UDS. One retired Portable Kitchen grill.
Red Thermapen, Maverick ET-732, EdgePro Apex Sharpener.
Avatar is the original 1951 Weber Kettle