I have to wonder... once the Dragonborn activates the portal to Sovngarde, would your average mortal Nord (or any mortal being basically) be able to simply walk into this portal and be transported to the paradise they keep longing for in life? Without actually having to die in battle?

(Let's just temporarily push aside the fact that it's pretty much impossible for the average man to even set foot on Skuldfan unless... you know... some kind-hearted dragon offers him a lift )

Also, I realize that simply walking into Sovngarde doesn't really mean anything because one can't get past Tsun and therefore into the Hall of Valor, where all the McDonald's... er I mean, all the eternal roasted ox and mead are.

Would he be able to just roam around the fields of Sovngarde, by simply walking into the portal?

One does not simply walk into Mordo. . . er, I mean, Sovngarde.

1. remember you need to go on a dragon up there, so i doubt any other nord(sovngarde, duh, i mean i doubt a khajiit decides to go up there unless he is dragonborn.)
2.if a nord wants to go to sovngarde just die in battle

3. One does not simply walk into Mordor. i agree

I guess so. It's (apparently) just another plane that also happens to function as an afterlife, and anyone was able to waltz on in to the Shivering Isles. I imagine the portal was probably closed after Alduin's defeat. Perhaps he even created it himself, eating a hole through space.

What, really, is keeping anybody from just hiking up into the valley? Unless the place itself were airborne there seems no reason why one couldn't. Who needs a dragon when you have a rope and some nice climbing shoes?

Location, location, location. It's in the middle of nowhere, in the mountains, invisible from ground level. Even if the Dragonborn could discern an exact location from the air, and then chose to divulge it, the fact that we don't close the portal doesn't mean it stays open once Alduin is gone. And the only way to return is when you are Shouted back, portal or no, so it's unlikely any would return to tell about it if it was possible.

Also, there's no climb skill anymore, dude. Phsaw, that was like four games ago.

As for the entering of Sovngarde via the portal, I wouldn't be that surprised. Nords have been trying to find their way in for millenia, since the belief that heaven is a place on earth seems to persist among traditionalists and imperialists alike in the face of all that the scholars can throw at them. But considering the way Nord stories work, it's honestly surprising that one of the great heroes of myth hasn't actually visited before. I'm willing to bet that Talos himself probably flew in for a chat with a ghost since he was too arrogant to just pay the medium.