Veracruz sits in the middle of the Gulf of Mexico, it normally has a very hot and humid weather, being south of the Tropic of Cancer at sea level.
Year round dress code includes t-shirt, short, sandals and maybe a cap or hat. But during Winter months there are the "Nortes" or "winds from the North" some of them can reach gale force and be unpleasant and a bit dangerous, a "regular" one can have winds of 80 km/h and gusts of over 110 km/h. but strangely, local people continue their lives as if nothing. Me as a tourist was trying to stay inside at all times but life keep flowing almost as normal. The biggest problem with such strong winds is that it carries lots of sand, so if you stay out in the street for a long time, you won't need to get a "peeling treatment" at your Spa, you skin will be sanded for free, so your bare legs and arms but it's a bit harsh, so beware and carry a handkerchief to cover your nose and mouth and your sunshades.
Fortunately "nortes" are very well know in the area and people gets early warning a couple days before they strike the area, this is one of the few times meteorologist don't go wrong.
When a Norte is striking the best thing you can do is enjoy the food at one of the numerous excellent restaurants, visit the aquarium or go to the movies. The rest of the attractions may be open but you won't enjoy them as much, the majority of them being at open air.
BTW, if you hear that a "Surada" (winds from the South) is coming , it means you will enjoy warm winds coming from the Equator. They normally are not as strong, but you should always be alert.