Meaning
Besides making cold, in Patois 'freeze up' means to become stiff with fear, shock, or nerves — to seize up and be unable to move or speak. 'Him freeze up wen him see di duppy' means he froze in terror. It can also mean to give someone the cold shoulder.
Examples
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She freeze up wen dem call har name.
She froze up when they called her name.
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Di bwoy freeze wid fright.
The boy froze with fright.
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Since di argument dem a freeze mi out.
Since the argument they've been giving me the cold shoulder.
Origin
From 'freeze'; extended to seizing up with fear/nerves, and to snubbing ('freeze out').
How it’s used
'Freeze up' = seize up with fear/nerves; 'freeze out' = snub. Compare 'frighten', 'breezy'.