Monday is a bit of a confusing holiday/non-holiday. Not just because of its being called Columbus Day or Indigenous Peoples’ Day, but because it is a federal holiday but not a state, city nor county holiday.
In other words, all non-essential federal government offices (i.e., U.S. Postal Service, Social Security Office, passport office, federal courtooms, etc.) will be closed.
On the other hand, The NYSE and the Nasdaq will be open, but the bond markets and most banks will be closed.
Regarding the city, county and state offices like the Department of Public Safety and Dallas Animal Services — they’ll be open for business.
As for schools, some are open and some aren’t, so check with your school calendar.
Guaranteed to be open: retailers, restaurants, movie theaters and the State Fair of Texas.