For instance:
An ice specialist would receive most of the usual spells, the main spell all the specialists sharing is hellstream. The ice specialist would gain something like icy veins which enhances the effectiveness of ice spells whether it be more dmg, reduced strength, -1 attack from being cold.
There could different forms of firestorm, via a true icestorm (like firestorm but ice), the ability to have enhanced ice shield which could possibly add a bit extra to ac.
Even though this is a specialist in the art of ice, it would share some magics with those of the other trees (exception of the stronger specialized spells and at perhaps a slighter weakened strength.
A special ability could be something small as giving each specialty something towards their respective tree.
Fire = burns (damage upon movement, scratches between moving rooms for an hour or 2, your so badly burned your skin is melting off with each movement)
Ice = frozen blood (-dex and -str for x amount of hours, your body struggles through the immense cold)
Wind = bruising (-int and -wis for x amount of hours, your skull was bashed around from the gusts of wind)
Lightning = static shock (slowed regeneration for x amount of hours, your heart struggles to handle the charge)
Just a few examples. Not actually sure if worth a ****, just off the top of my head.