Yes, Nevis is in the tropics, but it is a small island cooled by almost constant breezes off of the ocean, so it never gets really hot. The weather also doesn't change much all year round on Nevis, except during hurricanes, which are infrequent (the last one to really affect Nevis was Lenny, 1999, and there was a brush with Omar in 2008). 

The Atlantic side of the island has stronger breezes than the Caribbean side, and the higher up the mountain you are, the cooler the temperature is, and the stronger the breeze is too. When you are high up, you are more likely to get evening or early-morning showers, as clouds usually form around the peak of the central mountain, Nevis Peak, especially at night.

The winter temperature averages 79º F (26.1º C), with daily ranges from a low of 75º F up to a high of 85º F.  Wind speed is usually about 10 – 15 mph, but can get higher during December for a few days, as the winter solstice passes.  Winter is the ideal time for people to escape the frigid north and enjoy the lovely warm seas around Nevis.

The summer temperatures on Nevis are also good, being only 3º F higher than the winter, averaging 82º F (27.8º C). Winds are usually less strong in the summertime, except of course during tropical storms or hurricanes.  Because there is less wind, the ocean water is calmer and slightly warmer, so summer is ideal for diving.  And because the climate on Nevis never gets very hot or very humid, summer is also a good time for people from the southern parts of the USA to leave behind all that stifling heat and humidity. Nevis beaches are never crowded, and both airline rates and hotel rates are cheaper in the summer. 

In terms of what to wear, shorts and thin tee-shirts are OK for outdoors. But this is the tropics, so if you prefer to be cooler still, bring loose-fitting, woven (not knitted) clothing, made of light-weight cotton cloth, or better yet, thin linen cloth. Linen shirts and dresses are the coolest of all because they allow the breeze to blow right through. A suitable sun hat of some sort with a brim is an excellent idea, and don't forget to bring your sunglasses, and lots of high SPF sunblock. Skin used to more northern climes can burn very quickly indeed in the tropics, and a tropical sunburn can be quite painful, so be careful with this, especially if you are outside in the middle of the day. Whether you are male or female, a man's long-sleeved thin cotton shirt makes an easy and comfortable cover-up for beach or snorkeling.

An umbrella is generally not needed, although you may encounter the occasional shower, more so in summer than in winter.  If you are sensitive to cooling off, and are staying on the Atlantic coast (which is windy) or up around 1,000 feet (which is much cooler), then you may find that a shirt with long sleeves is more comfortable in the evenings.

If you are going to be staying at one of the elegant, upscale hotels, then in order to be dressed appropriately for dinner, men need to bring a pair of long pants (not jeans, not shorts) and a couple of shirts other than tee-shirts (no tie or jacket is needed, and Hawaiian shirts are just fine.) Covered shoes rather than flip-flops are also part of the dress code for men. For dinnertime at the upscale hotels women need to bring a dress, or a nice skirt and blouse, or nice-looking pants. No shorts or jeans at dinner, and no tee-shirts. There is a strong tradition of dressing up a little in the evening at the fancier hotels, and with the oil lamps burning, the stars twinkling, and the soft tropical breeze blowing, it all makes a for an elegant, old-fashioned Caribbean evening.

The photograph shows the view from up on the mountain, on a sunny day with some small scattered clouds.