Space, Reach, & Threatened Area.
Scroll down and you'll see the 'Creature Sizes' table.
'Long' creatures have less reach than 'tall' creatures.
Mounts are generally 'Long' creatures, and suffer from less reach.
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The issue is that bestiaries don't have explicit rules on what makes a creature "Tall" or "Long"
You can typically infer based on whether or not it's a quadruped (or more) or a biped; bipeds are typically shown as "tall" like giants and creatures with 4+ legs are typically shown as "Long" like Dire Tigers.
This rule is broken seemingly at random throughout the bestiaries, however. Take Triceratops, for example. According to the Huge(Long) template like you might think a triceratops falls under (since it's a quadruped usable as a mount), it should have a natural reach of 10ft. However in the bestiary entry it has 15ft reach, under the Huge(Tall) category. It gets even more confusing if you have a Triceratops as an animal companion: Prior to level 7 your dino is medium and it's pretty clear that it's just a 5ft reach, but at level 7 it's large size, which doesn't have its own bestiary entry. Without the Companion entry stating whether it has increased reach, by RAW, the triceratops only has 5ft reach as a large animal companion. Throw on an Animal Growth on it and it's huge but the reach is still only 10ft.
It's a problem I've never seen formally addressed.
But to answer your question, the wolf has a 5ft reach when it's large; the bestiary entry shows that it falls under the Large(long) category and as a result your animal companion does too.