Using 老头 / 老头子 when speaking to others
The counterpart of 老太太 could be 老先生. It has a sense of showing respect. You can also say 老奶奶 (female) and 老爷爷 (male), which is more neutral.

Personally I feel 老头 is impolite, especially when combined with "一个" as in "一个老头". I'd rather use 老人 to say 我今天看到一个老人在喂鸽子, of course, this doesn't imply the gender of the old person.

老头子 is more commonly found in how an old woman calls her husband... Depending on the context it could have positive or negative connotation.