Its totally do-able if you have the right tools and materials to do it.
Commercially spun wool yarn is readily available for purchase in a huge variety of colors and weights.
Or you can spin your own. You will need 2-3 full fleeces, for both warp and weft, and depending on the size you want to make. Combs or cards to process your clean wool, and a drop spindle or wheel to spin it all on. Plus months of continuous spinning to make enough yarn to weave it. I suggest a minimum of a 2 ply yarn for this project, 3-ply will hold up better and be slightly warmer though.
If you want the points woven in, you will have to find some natural color wool or dye some so you can weave your stripes in.
You will need a loom. A Hudson Bay blanked is a simple over/under weave structure. So you need a two harness or even a rigid heddle loom to do that weave. Based on how tight Hudson Bay blankets are woven (i'm looking at a modern one, not a "home" woven one) you will need something with a metal reed in it so you can beat it tightly. A plastic reed, such as what they use on modern rigid heddle looms, I suspect wont stand up to that kind of use.
As noted above, 18th C blankets were two woven panels stitched together to make a blanket wide enough to be usable. Looms were much smaller in weaving width to accommodate smaller houses.
Feel free to ask any questions you may have!