The Greenbelt is there to…

The Greenbelt is there to protect against urban expansion, not to just be tossed aside when it becomes inconvenient.
Find another way to develop. Stop putting in infrastructure that is inefficient at stopping urban Sprawl like suburban housing.
You're worried about homelessness and unaffordable housing? Maybe try subsidizing rent. Building apartments that are actually affordable to the average citizen.

The environment is not something we can just do away with when it's in the way. Have we learned nothing from the years of incrementally hotter summers and winters?
Don't be lazy, come up with a more intelligent solution