adding a wireless access pint

Really depends on how far away the pole barn is.  Ideally, you'd just run cat 6 to the barn if it's 100 meters or less, then plug in your access point inside the barn.  You can get outdoor shielded cat 6 and bury it under the turf.

A lot of access points are PoE (power over Ethernet).  Xfinity gateways don't have PoE jacks, so you'll have to use a powered adapter.  Make sure it comes with one.

Distance with an outdoor access point?  Meh, it varies.  Can be slow too, or unreliable.  Metal buildings are not good for wifi reception, especially at a distance.  Wired to the barn, access point where you need it is better.

If it's a long run, you'll need a point-to-point bridge.  A pair of devices that do it.  Cost on those goes from around $100-450+ depending on what you need and what you want to spend.  If they say 5 kilometers, it's probably not all that true, and they have to be direct line of sight usually.