I'm worried about rain, snow, dirt tracking thru the house. Never have lived where there is snow so have a few months to figure it out

In snow country, homes tend to use a particular entrance during the snow months, where boots can be removed at the door. Sometimes that is at the side of the house, near the kitchen. Is this a house or a townhouse? Is there another entrance?

I would undo the carpet on the stairs, put a runner in black that covers the middle of stairs and leaves the sides with white painted wood showing and then re-tile the little area with black tiles. It's a tiny area but it could work better with a visible connection up the stairs.

of yes and I like the miacometlady's suggestion of mini mudroom but would myself consider the fact that it opens to the living room so something to cover up would be good. Maybe a black and white mud room covered with a "theatre" curtain in rich yellow (slightly clearer and and more vivid tone from the wall paint color) in heavy velvet, that could be pulled on the side with a robe?

This is my last comment, I promise! :) Coming from Finland, where most of the year the weather demands practicality, I think that the tiny tiled area is very necessary. You should tile the closet floor as well. Also an outdoor doormat with a possible boot brush would be good.

In Finland we leave the shoes that we use outdoors in the closet, that solves a possible problem without ruining the beautiful wood floors you have.

The mudroom is a great idea for family, but it doesn't always work with guests coming in. Since the entry leads directly into the wood floors of the living room, I would suggest that you get an indoor/outdoor small rug to use doing the winter months. No one can fault you for a rug to keep your floors nice and pick one that is functional but will blend in. Does the outside entry area provide for guests taking off their boots? Or do you keep the outside entry way weather proof so people do not tract into the house rain or snow?

There really isn't much you can do with the entry, since it is so small. It would have been nice if the wood would have continued in there. A round rug that is the appropriate scale is about all you can do. Maybe make it out of the stair carpet and have it bound?

Thanks for your comments! We do have a 3-season room at the back of the house where we can enter. The mini-mudroom is a nice idea but it would be so mini, it's only 36" wide and would be visible to LR. The brownish color on stair wall is going away and I"d like to replace the tile. Does it make sense to put a runner over wood in LR? I was thinking a bench on the wall

And, sadly, there is no overhand or portico over front door! That's something we didn't even think about when we bought the house.

Yes, I would use a runner. Are you adding a rug to the living room to define the area of your furniture? Would a runner interfere with it?

right now we have a cowhide in the actual furniture area (where we don't have any furniture lol), a runner wouldn't interfere

If you come in the door during the winter, I would hang your hat, gloves, coat up in the closet, sit on the step and take off your boots (and have a rug for them to dry on). If you came into the living room to do that, you would be wiping wet floors constantly. I would use a runner even if you do take your boots off in the front entry. Some folks eventually add on a small enclosed entry if the winters are severe. Looks like you have a lovely home.