We had one of those open tread staircases in our rental house, spiral to boot. For dogs who are not used to them, your assumption is correct: A bit of training is often needed.
Going up was easy for mine, including Psychocollie (who came by his name honestly
) but going down posed problems.
For a curious well balanced dog, free-shaping with the clicker, rewarding whenever the dog makes a move towards voluntarily taking a step down, worked well. After the first session Swimbo was trotting up and down without a thought.
Psychocollie needed more training, though. And support at first. On lead, lure with treat, click and reward each step or even each voluntary attempt. No discussion and certainly no recriminations for reluctance. And watch stress - literally take this one step at a time, stopping if you think the dog is too stressed.
But even Psychocollie got it in the end.
Fast forward 5 years, Psychocollie started to lose his back legs. Slippery wood surfaces were particularly difficult - including the staircase. I had already put sisal rugs down all over the house to help him, so looked for something similar for the stairs.
(Looking back, I wish I had thought of them when initially training the dogs to use the staircase.)
One of the issues we had was that the landlord was a carpenter, made the stair case himself, was very proud of it - and he was concerned that anything stuck to the stairs might damage the finish. I went directly to him for recommendations as well as permission for anti-slip matts, as I though his input would limit concerns later. I can't remember where they were bought, a local carpet firm IIRC. But such things can be found all over, for instance here from Amazon.de, deliverable to Switzerland: http://www.amazon.de/Teppich-Stufenm...treppe+Teppich
(Random google for Hund + Stufenmatt, no experience with this retailer.)
A side benefit of stair tread covers is that you also limit damage from the cliquey-clack of canine nails... something that should be pointed out to a reluctant landlord.
If this turns out to be your dream house, I wouldn't see the stairs as a deal breaker - Rusty seems like a quick learner.
(But any time you have stairs to get in and out of a house, think ahead 10-15 years. If you think you will still be in this house, do you think you will be able to carry your future elderly dog up and down stairs? )
Is this a rental or purchase?
If a purchase, and if the stairs are wholly yours - could you put backs on the steps?
I've looked at a few houses with what I thought of as problem stairwells (problematic for my wonky dogs, that is) and my husband though that adding a back to the open stairs wouldn't be too difficult of a project. Now, OH tends towards the overly optimistic when it comes to his DIY projects, but still... if you own the stairs, there are more options available.
IIRC, Mrs Doolittle had posted about stair solutions some years ago - you might contact her.