I would think the jostling from horseback riding would be uncomfortable with a PICC no matter where it is inserted in the arm or how long it had been since it was inserted...Also, you would not be able to lift things heavier than a certain amount (without risking damage to the PICC line)...and I wouldn't want to try to reign in a runaway horse with the arm with the PICC in it...definately discuss with your doctor!
I've had my PICC line for 19 months and I still have trouble doing some simple/basic things with the arm with the PICC. Showering is also a challenge, though not impossible.