I wouldn't use any of the fabric glues on it. It can't be done invisibly because there are no overlapping flat surfaces, and you couldn't get it out of the wool once in.

You have two alternatives: If you stop into a sewing store, or perhaps even a Walmart, you can get needle and some button-strength thread to match, and give it try. I wrote some instructions below, on how I would mend it. Your other alternative is to take it to be mended, which would be inexpensive and completely worth it for a Pendleton blanket. Most dry cleaners have someone to do mending like this.

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This may be slight overkill, but one wants something sturdy for a blanket. Thread the needle, pulling the thread double, and knotting the two threads at the bottom. Begin sewing on the wrong side of the blanket, passing the needle through the bottom of that loose edge (the part that is already overcast with thread) and wrap the thread around that same bound edge, and come back up between the two threads to anchor it.

Then it is simply a matter of overcasting between the bottom of the loose edge and the blanket, around and around to secure it, making sure you far enough into the blanket to get to the securely woven part of the fabric. I would do extra stitches at the outside edge for strength.

When you have done this, with the thread on the right side, cut your thread in two by the needle. Then rethread one thread, and pull it through in one place; remove the needle, go back to the other side and rethread the other thread on the needle, poking it through in a slightly different place. Tie the two ends to anchor. You don't usually need to do this for mending, but given a blanket is a coarse weave, it will be the most secure.