Yes, You Can Attack
The Minotaur can attack at 5' and 10' using its Gore attack. It can also attack at 15' and 20' using its Guisarme, as per the reach weapon rules (emphasis mine):
Glaives, guisarmes, lances, longspears, ranseurs, spiked chains, and
whips are reach weapons. A reach weapon is a melee weapon that allows
its wielder to strike at targets that aren’t adjacent to him or her.
Most reach weapons double the wielder’s natural reach, meaning that a
typical Small or Medium wielder of such a weapon can attack a creature
10 feet away, but not a creature in an adjacent square. A typical
Large character wielding a reach weapon of the appropriate size can
attack a creature 15 or 20 feet away, but not adjacent creatures or
creatures up to 10 feet away.
When you increase the reach on reach weapons, both the attackable range and the dead zone (if it has one) increase. So the weapon goes from a 5' range and a 5' dead zone to a 10' range and a 10' dead zone.
This means the Minotaur can attack and take AoO's anywhere from 5' to 20' away. It would use its gore at 5' or 10', and Guisarme at 15' or 20', using the relevant attack & damage rolls. If it lost the Guisarme, it would only be able to use it's Gore at 5' to 10'.
Pathfinder - The Same
The result in Pathfinder is the same. Here's the relevant rule, for larger creatures with reach.
Unlike when someone uses a reach weapon, a creature with greater than
normal natural reach (more than 5 feet) still threatens squares
adjacent to it. A creature with greater than normal natural reach
usually gets an attack of opportunity against you if you approach it,
because you must enter and move within the range of its reach before
you can attack it. This attack of opportunity is not provoked if you
take a 5-foot step.
Large or larger creatures using reach weapons can strike up to double
their natural reach but can't strike at their natural reach or less.
The Minotaur also still has its large size and Gore attack, so there's no difference there.