You can correct this problem in two ways.
1) If it is a stall blanket with a center back seam, remove the wither pad and the edge binding at the center back seam, then put the blanket on the horse. Lift & pin a new center back seam, starting with the neckline edge and angling back to the original seam so the the new seam will lay flat, and the front of the blanket fits the horses chest correctly. Take out the stitches from the old seam, and stitch the new seam, then finish the new seam the same way the old seam was finished, removing the excess. Put the edge binding back on, overlapping where necessary, as you will have more binding than you need.
2) If it is a T/O, the above method won’t work, as 99% of all T/O’s do not have a center back seam, as it could leak. Instead, put the blanket on as above, but add a dart on each side, right at the inside corner, where the neckline changes direction from up/down, to across the front of the chest. The size of the dart will depend on how much too big the chest area is for the horse. Once you have established how wide the outside edge of the darts needs to be, remove enough of the edge binding so that you can pin each dart flat and stitch it down. Reattach the edge binding, over lapping the edges, as you will again have more binding than you need. You may need to trim the excess binding, in which case you will want to turn under a 1/2″ or so of the top layer of the edge binding so that the binding does not ravel.
If you don’ sew, but have a good blanket repair person in your area, you can do the measuring & pinning yourself, but have the blanket repair person do the sewing, as they should have the more powerful commercial sewing machines that may be needed to sew through all the layers.
Either of these methods will work for T/O sheets, light weight T/O blankets, and medium weight T/O blankets. Method 2 does not work well for heavy weight blankets as you end up with too thick a dart that will not lay correctly flat. Unless you want to remove excess fiberfill, which is more work than it is worth. You can always add a blanket liner for really cold days, but you may have to alter the liner in the same way.
This is actually a very common issue. Some blanket repair places know how to custom fit blankets, some do not. But if you pin the darts in for them, they should be able to do the sewing part. I custom fit a couple of blankets almost every winter.
My other suggestion is to look at the Dover Northwind line of 1680 T/O sheets & blankets. They are fairly expensive, but well made and the entire line has extremely small chests, so they tend to fit some of the narrower chested horses, but not breeds like AQHA’s or even a lot of the TB’s. But you won’t find that info anywhere in the on-line catalog blurbs.