Will the player with the mounted knight have fun playing in Savage Tide? Likely not, but it's not because the DM is running a "railroad". Its because the AP isn't well suited to that kind of PC.
Either the guy with the mount has the choice to go where his mount will be useful or he doesn't. If he doesn't have that choice, the GM is railroading.
Remove the railroad and the player's self-interest will take care of itself.
Now, the start of a campaign is a different matter. It's not a railroad to say "this is a campaign set on a chain of islands" or "in the middle of the desert" or "in the Underdark". The player can either design an appropriate character, deal with the consequences, or not play. The GM's only responsibility is to clearly communicate the concept, and the limitations of that concept are no more unreasonable than saying "you can't play a spaceship pilot in a campaign about modern FBI agents".
But you'll notice that, once again, freedom is given to the player. And they can use that freedom to address that issue in whatever they want.
The point is that the GM only needs to worry about being a nanny if he insists on treating his players like children.
Vehemently disagree with this. When I start a new campaign, the invites include my 8 house rules of which 1 and 3 are appropriate to this thread.
House rule #1 is: I run "adventure paths". You must be willing to follow the campaign premise and plot.
Well, then. You have a problem. You have created it for yourself by choosing to railroad your players.
Long story short:
(1) If you, as the GM, don't want the responsibility of catering to your players, then don't run a railroad. This allows the players to cater to themselves and you don't have to worry about it.
(2) If you, as the GM, want to railroad your players, then you have a responsibility to cater to them.
The third option is that you're railroading your players in order to prevent them from doing things they find fun and/or force them to do things they don't want to do. Why the hell would you want to do that?
Re: Mounts. Invest in some magic items.
Horseshoes of the Zephyr will open up quite a few terrains. A little ingenuity should allow for transportable extradimensional stables (similar to a
bag of holding, but with breathable air; or using a traditional
bag of holding while putting the mount in some form of stasis) or resizing of the mount to lead them through tight spaces.