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I'm running a game with a couple of friends, one of which is a druid with a base speed of 8, and the party has hired some horses (speed 10) but almost lost one in combat as an enemy tried to escape on it. The druid then said, half jokingly, that he could just run to keep with them if he had lost the horse since running gives a +2 to speed, assuming it applies outside of combat at the DM's discretion.

It's got me curious since the rules generally cover walking, resting and what-not; are there any rules/penalties that govern, I guess you'd call it fatigue outside of combat? or are there any suggestions on house ruling something like it?

Scenarios could include: running a message from one village to another and back, which might take the party an entire day or two if you include rests but might only take half a day for the one character running, or running into an encounter i.e from village to cave to fight a bear, or being ambushed.

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There is actually a rule for this (or at least close enough to one for this exercise).

Speed per Hour: A creature’s speed per hour assumes a walking pace. A creature can move at twice this speed for an hour. If the creature maintains the faster pace beyond that time, the creature loses a healing surge at the end of each subsequent hour (or part of an hour) at that pace, or it takes damage equal to its level if it has no healing surges left. (RC 169)

Basically, you can go twice your normal walk speed for up to an hour without costing yourself anything. However, if you push yourself too hard for too long, you'll start docking yourself surges, and then actual HP.

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Maybe you could add an endurance check before you start losing surges. –  Tijnkwan Jun 30 at 21:49
    
@Tijnkwan an endurance check is required before surge loss if a character wants to walk more than 10 hours in a day. Running twice your speed should be much more severe. –  wax eagle Jun 30 at 22:32

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