No one plays outside anymore.

The “too” is a reference to the other days of the week. The father doesn’t perform these actions on just the weekdays, but on “Sundays too”. I think a very apparent theme addresses the difference between a white collar job and a blue collar job.

There is reprise in the last few lines:
“What did I know, what did I know
Of love’s austere and lonely offices?”

It brings the situation to possibly more of a choice rather than submission. Maybe the father has no taste for the city life (lonely offices) and maybe had true passion for the work that must happen every day (love’s austere). This is a reflection, it seems, as the Author expresses, “What did I know…” All of these ideas that the child assumes for his father’s occupation, whether it is out of submission or out of choice, beyond the child mind. The child is too young to see the reasons. He only sees that it is cold outside, and it’s not fun.

I relate this to living in Utah. Anyone could live in California with nice warm winters, and view Utah as just cold, not only in a weather sense but also in cultural context. In fact, many people do view many places as just “cold”, but are often oblivious to the Idea that people do things for reasons. We live in Utah for reasons. The father goes out in the cold on those Sundays for a reason.