I have the Polo Ralph Lauren logo on the left side of my shirt. Is it permissible for me to pray salat while wearing it?
Yes, it is permissible. The face of both the horse and the rider is unclear in this logo. Ibn Abbaas (RA) said:
"The image is the head. So if the head is cut off, it is no longer an image." -- Source
Shaykh Ibn Uthaymeen said:
"If the image is not clear – that is, it does not have eyes, a nose, a mouth or fingers – then this is not a complete image and is not competing with the creation of Allah, may He be glorified and exalted."
Quote from, Majmoo Fatawa ash-Shaykh Ibn Uthaymeen (2/278-279)
Since the image is not haram, it is halal for you to wear this shirt and pray while wearing it.