In general are most divorced fathers happy during days, such as Father's Day, since they seem this way? Or, it may not be as simple as this?

Depends. Father's Day for a divorced father will reflect his unique relationships with his children, ex-wife and significant others. If there is ongoing conflict, it may be heightened as expectations for Father's Day can run high. If relationships and personal circumstances are stable and time with children have been working out in the past, the day should be a pleasant one. Patterns tend to continue.
A father. is always a father, whether or not it's Father's Day.