leave someone cold—fail to impress or interest a person:
- An orator may discourse very eloquently on injustice and leave his audience cold.
leave someone out in the cold—ignore or abandon smb.:
- Developing countries might be left out in the cold in current world trade talks.
Note: The expression does not fully correlate in meaning with the phrase leave someone out—
1. = leave someone out in the cold:
- It’s Mary’s own fault if she feels left out at the party; she makes no effort to be friendly to people.
2. fail to include a person (in a list, etc.):
- He toasted all the other ladies present, but left Jane out.