Is the purpose of the second sentence to restrict this card to one play per turn as the first action modifier for any action? Or is it only usable as a hunt modifier?
Start your minion phase.
First off, you'll be taking any mandatory actions. (If you have a mandatory action to take, you must order it before non-mandatory actions.) This includes hunts by empty vampires, but also includes other mandatory actions such as Cry Wolf's mandatory rush, Lunatic Eruptions's mandatory rush, Triole's Revenge's mandatory hunt, and Philippe Rigaud's mandatory diablerie.
If you have a whole sequence of these mandatory actions, you can play Uncontrolled Impulse on any or all of them.
Once you've run out of mandatory actions, you go back to non-mandatory actions. So, you equip a Hawg (for example). The only actions that have been performed so far this turn are mandatory ones. So you can play Uncontrolled Impulse on this equip. (Or bleed, or vote, or whatever other action you've chosen.)
After this, you might be performing non-mandatory actions, or possibly new mandatory actions (e.g. you've taken a Blood Brother's last blood with a Sanguinus card, so now he has to hunt). But since you've taken a non-mandatory action - equipping a Hawg - you now can't play Uncontrolled Impulse on any of these actions.
1) Start the minion phase
2) Take one or more mandatory actions - Uncontrolled Impulse playable on all of them
3) Once you've run out, take one non-mandatory action - Uncontrolled Impulse playable on this action
4) Take any other actions - cannot play Uncontrolled Impulse, because of the action in 3)