It is absolutely instinctive for horses to be afraid of pigs. Whether this goes back in the evolutionary chain to when they were much smaller and wild boar preyed upon them, I don't know. However, pigs can be pretty vicious if annoyed, and so their fear is entirely justified.
If you would like your horse to meet pigs in a safe environment, then Longdown Farm have given me permission to use their premises during the closed season which runs all the way through January and up to February half-term. The price for a half day session is £150 inclusive. Other animals are also available!