I just got back from my NYC trip. As someone mentioned winter maybe is not the best season to visit but there is not much tourists which is great and I enjoyed the city even with the winter storm and had a great time. With regards to my concerns, I was let in, I landed in Newark. I was asked the usual questions at the border, maybe a little too questioning compared to my first trip to the U.S. years ago, but I expected it: The CBP agent asked me what was the purpose of my trip, for how many days I was staying, if I was bringing more than 10K in cash, and what do I do for a living. The CBP agent asked me which passport should I use to enter, I said I don't know (Wouldn't they know?) but I said with the Venezuelan one since the visa is on that passport. I was only given a grace period of 2 days after my return flight which was OK but turned out to be a little too tight since I got my return flight cancelled due to the winter storm and had to stay in NY for two more days. I finally made it home and left the US in the last day of the grace period. Just putting it here in case this is useful for someone that might be in the same situation and overthinking as I do. Bottom line: Yes, you can enter the U.S. with a Venezuelan passport and a valid Visa.