There's only 692 steps or something like that.
I envisioned the 7000 steps actually being one huge continuous monolithic ancient stone steps/stairs. But it's more like a path that swirls around the mountain until you reach the top, and a lot of the steps aren't even connected, or are and they're just buried too deep beneath the snow. Sorry for my bashing of the game. I played it for the first time last night and I was disappointed.
To answer the OP question, no I didn't walk, I ran the whole time.