I wouldn't be concerned about switching saddles, as long as the new saddle fits correctly. If the Wintec has the changeable gullet system, you have a pretty good chance of dialing in a better fit. I have swapped western for English on a horse with a mystery history, and he did better than me, lol. My new greenie I initially rode in a western saddle so I had a little something to hang onto if he did something unexpected, and he never skipped a beat when I put my English tack on him.
As far as the bit goes, if the horse is used to being ridden in a shanked bit for western and the English rider wants to ride in a snaffle, the horse may need a refresher course, but the horse should be okay, esp. if he was started with a snaffle, as most horses are. Again, I pulled my greenie out of a Tom Thumb (from his western ensemble...) to a single joint eggbutt snaffle and he did fine after a little circling and bending. My sis rides both styles, and rotates between a curb with a low port and copper roller for western and a solid mouth, low port Kimberwicke for English for her horse.
I hope that helped!
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown