walking to hotels from Heathrow?

If they are off Heathrow property then there is no safe walking route.

There are a small number of hotels attached to terminals at Heathrow, which you can obviously walk to, but most are outside the airport perimeter and there is no way you can walk to any go them even if they are only a mile away.
Obviously the ones attached to terminals tend to be more costly but they are a lot more convenient. The others need either a bus or taxi to get to and from.
You should also consider hotels close to Hatton Cross tube station. It's just one stop from Heathrow so can be both quicker and cheaper to get to than many "airport" hotels.

When I was in the area in 2018, there was a free bus zone around the airport. I took the bus towards london, got off at the last stop within the zone and walked to the Premier Inn Bath Road. There were sidewalks, crosswalks and easy to walk. It was still about a kilometre, but I had no issues with it. I arrived as dusk was setting in and left in the morning before 9 am. It isn't fancy, but it did the job and had food on site.

The real problem is that there is a tunnel from Terminals 2 and 3, which has no footway. Even if it did you wouldn't want to use it due to the fumes.

The free travel zone has been contracted in size since as I have used the FTZ before.

This is the current map. The H30 bus mentioned in the text only operates between 2 am and 4 am, apparently, from reports I have read. Technically it is public, but is only really run for staff. https://www.heathrow.com/content/dam/heathrow/web/common/documents/transport/Heathrow-free-travel-map.pdf

There are however any number of public bus services out onto the Bath Road, every few minutes, 24 hours a day.

There is also, at a price, a Hotel Hoppa bus service.- https://www.hotelhoppa.co.uk/

Sofitel at terminal five is a favorite( and a bit of a splurge).

The Heathrow free travel zone has lost the busses but gained Hatton Cross tube station which has a couple of hotels nearby. You do need a contactless payment method / Oyster card even though it is not charged.

If price is an object, check rates at the Premier Inn T4. You can use the underground to get between T4 and the terminal your flight uses. The hotel is a longish walk from the terminal, but the enclosed walkway is connected to the terminal. There is an elevator (maybe one on both ends of the walk) but no stairs. The hotel is newish and very large. Rates are usually extremely low for a hotel located right at the airport and considerably lower than Premier Inns in downtown London. There are three different cancellation options for Premier Inn reservations; I always choose the most expensive one.

The Heathrow free travel zone has lost the busses

So I take this to mean bus 423 (I think that was the number) is no longer free to/from T5 and several other stops along Bath Rd between it and T2/T3 ... time to refigure that evening stay and dinner plans.

No 423 isn't free because it goes 'off site' between terminals so £1.75 each journey, £5.25 day cap.

Ok, thanks for the info ... staying at the Premier Inn T5 so all is good getting there and back the next morning ... planning on going to The White Horse Pub for one last British pub meal, looks like they have a van that will pick you up and drop you back off at your hotel, plus it's only an 8 min walk from the Premier Inn so we're good there also ... crisis averted.

It is absolutely NOT true that you cannot walk to any off-airport hotels. It is just that they are not "right next door", rather 5 or 6 km away by foot for a lot of them. With bags, I think it is what they call a "non-starter"... Red buses are cheap, and they go right near all the hotels. The Thistle Hotel is an exception, reached by driverless Pod, the cost of which is added to your room.

There are a few You Tube videos of people walking or cycling around the airport, so you can see what might be involved. One other issue is that some buses put you on the wrong side of a busy road (Northern Perimeter Road, and Bath Road), and the crosswalk might not be nearby.

There is a nice and relatively new Hilton Garden Inn between Terminals 2 and 3. And an even nicer Hilton at Terminal 4. These can all be reached by foot. Both hotels are exceedingly well sound proofed.

OK, for Phoffen- I will qualify that,
From Terminals 2 and 3 it is not possible due to the tunnel.
Phoffen has been looking at videos of people from Terminals 4 and 5 which you can walk out of.
But as most of the hotels are on the Bath Road/Northern Perimeter Road it would be plain bizarre to walk miles and miles round the airport or take a very roundabout bus route when you can take a free train to Terminal 2/3 for the Central Bus Station where most buses leave from and are on the Bath road in minutes.
Perhaps if the OP told us which hotel the question could be answered definitively.

We are staying at the Renaissance Inn, Hounslow, on Bath Road.

Basically we want to be sure we can get to the hotel quickly enough to drop off our luggage and head into central London. We arrive at 2:30 and leave the next day at noon, so we don't want to waste a second!

Thank you to everyone who has posted advice and information! It is most helpful!

That is unwalkable due to the tunnel. Every few minutes bus 111, 555, 105 or 278 getting off at Nene Road, then a 7 minute walk, or various of the Hotel Hoppas go to the front door- notably the H2X goes there (only) from T2 arrivals and T3 arrivals, half hourly until 2310.