I haven't shipped one from Texas but did from Indiana. And you have to be careful as far as quarantining them goes. I believe that when bringing a horse into Canada that you have to have them quarantined for 90 days depending on which state you get the horse from. I think Texas is one of those states that you have to have a horse in quarantine for 90 days before bringing it to Canada. You can check online though.
I had no issues at all with bringing my filly from Indiana, you need vet checks, coggins etc. I made sure I had lots of insurance on her in case anything was to happen in the shipping etc. I lucked out though the lady I bought the filly from brought her so far and then another couple brought her to Skowhegan Maine for me and I picked her up there. But to use a shipping company I have no idea.