I had a very similar experience bowhunting on some private land at least 20 years ago. I hit a nice 4x4 (western count) whitetail buck out of a tree stand, and had some good snow on the ground after a light storm the night before. Arrowed the buck, and he ran off and was out of sight. Waited a while in the stand to let things settle down (me mostly), and then climbed down. There was good blood to begin with, and then, as it turned out, there were two other blood trails, crossing mine, from other hunters from that same morning.
I never saw either of those hunters, but by the time I realized there were more blood trails than my own, the snow melted off, and I lost my trail. I trailed MY deer a good, long distance from where I arrowed it, but I was sick that I lost my deer after looking most all that day.
About a week later, one of the local high school kids who shot bows with a small group of us "old guys" (that was a really cool little group; respectful school kids who wanted to learn) asked me if I shot at a buck recently over in the area I hunted (he had permission to hunt there, too), and I surprisingly told him I had. He then told me he found a dead 4x4 with what he thought was my arrow (an Easton XX75, 2216 shaft with green and black vanes). From our close little group, we all knew what equipment each of us was using to hunt with, so he knew my arrow! Since we both knew the area well, he told me where he found the deer, and I went to look for it. Sure enough, there the buck lay, with my Easton shaft buried in its side. To the young school kid's respectful credit, he never touched the deer, nor the arrow, but wanted me to know he'd found it, which he did. And here's the kicker to the story; after my looking for that deer, which took me close to a half mile away from my stand, and then losing the trail, that whitetail buck was found dead by my young hunter friend not 60 yds. from my stand. It made a gigantic circle back to where I'd shot it. It was a lesson, certain sure. Because of what I went through losing the track, and then the the fine kid who found it and told me of it, I punched my tag on that deer, cut the head off the carcass and went home. Didn't make deer meat that year, but the whole story, to me, was worth the meat loss, and the use of my tag. And, of course, I still have that rack...
That young man who found my deer graduated from high school that year, and I never saw him again, even to this day. But a year later after my bowhunting incident, my oldest son got out of the Army and it was fall of that year (late 90's) and thought he'd like to hunt a whitetail. I got permission for him to hunt that area I bowhunted, and he was allowed to rifle hunt in there, and he used my old .32 spcl. M94 (my old deer rifle, his now) and he shot a nice 4x4 not but a 100 yds. from where I arrowed my buck the previous year. Now here's the kicker on that story; that deer had an arrow stuck through the meaty part of the neck, which was not any kind of a killing wound, but it was a good find for my son to shoot, and he made a fine kill shot with the old .32 spcl. Very odd with the arrow in the neck, and here's the next part of the story. That arrow, I identified as an arrow of one from the SAME KID WHO FOUND MY DEER THE YEAR BEFORE. No freeking kidding. I knew it was his, and I couldn't locate him to give it back, and tell him the story. Sheesh, you really can't come up with these sorts of things without some fantastic imagination from a novel. And one more time, to this very day, I've never seen that fine young fellow bowhunter who found my deer all those years ago. I had that 2018 Easton Game Getter shaft, with a Bear Super Razor head tip for a long time, always meaning to get it back to my young friend, and never did. And now, I hate to admit it, but I have no idea what happened to that arrow through the years of moving it around, and then moving to a new place 10 years ago. Just a hunting story here, to go along with the OPs deer. So glad you found it, hope the meat was still good, too.
And as a parting shot here, I live in Wyoming, and I just came across a new addition to the 2020 big game hunting regs. that now states that one leashed dog can be used to track a wounded big game or trophy game animal for 72 hours after the wound/shot was made by a hunter. That's pretty big news for a new addition to the regulations. That will no doubt make a big difference in finding a lost animal.
If you're a hunter long enough, you'll have a critter that eludes finding it at some point. I've been a big game hunter for over 50 years, and have lost a few critters in that span of time, and it's always a lesson, and it always makes me sick for the loss. Hope everyone's hunting season has gone well, and hope it continues successfully through the year!