I don't have a Chinese-English dictionary with me. I wonder what they translate the word 怕 to. You can't say fear or be "afraid of". A proper word may be "be sensitive to". So here's my translation:
"I'm skinny. I'm sensitive to cold (or cold weather). But I'm OK when I'm hot [or when it's hot]."
But that may be too literal. You could simply say "I don't like cold weather", or "I don't feel comfortable when it's cold", "I feel cold when it's cold".