There is definitely a difference in clothing due to regional weather. The biggest difference comes in the choice of fabric. Adjusting the layers helps to deal with cooler weather, but one can only take off so much before you've exposed yourself to the sun and things get worse instead of better. As for fabric, linen and cotton are generally the textiles of choice for hot weather, though lightweight silks and wools in light colors do well. At the very least, they do far better than our modern synthetics. Seasonal clothing was very necessary, more so than today with our controlled interiors. The person wearing jeans and a black t-shirt on a 90 F day is going to be far hotter than a woman in her 18th or 19th century fashions.

Simply adjusting the textiles means that the fashionable cuts, styles, and trims don't have to be lost just to deal with the weather. It did take a while for some of the first colonists of the Caribbean islands to loose their grip on the fashions of heavy wools, silks, and velvets from cooler Europe. Remember that in the earliest times they didn't have a plethora of tailors or mantua-makers in the area who could make clothing to suit the local weather. They were still importing from their tailors back home. Once we establish an economy in a location, the tailors show up very quickly and adjustments are made. Agostino Brunias did a series of paintings about life in the West Indies near the end of the 18th century. They're still wearing the standard fashionable items, but all in light colors and guaranteed linen or sheer cotton. There's evidence these fashions can be cyclical and came back around to influence the Chemise a la Reine style which Marie Antoinette wore in her infamous portrait. Getting a little specific, Neal Hurst wrote an article on Men's summer dress in Virginia during the 18th century that covers the sort of alterations made well.

As for colder weather, layering is key. Today we rely on a very heavy coat over clothing intended to work with 70 F interiors. Before modern heat/cool the temperature inside might only be a little warmer or cooler than the exterior. Flannel undergarments and extra layers like under waistcoats or under breeches provide the insulation needed. That cloak or coat worn outside is more to protect from the wind or precipitation than it is the cold.

To put it in a comparable situation a woman in 1780s Southern US will get up and put on a linen shift (which might be changed once or twice that day), linen stockings, summer stays or jumps (two layers of linen), a white linen petticoat or a quilted cotton one that doesn't stick to the skin, a white linen or cotton gown (unlined), a light kerchief to prevent sunburn, unlined linen mitts when going outside for the same, a cap to help keep the hair clean, and a large hat when going outside. I can't emphasis the light and sheer enough! To compare a woman in the winter up north would start with the same linen shift, silk and wool stockings layered, a flannel under petticoat, heavier stays, flannel waistcoat, one or more heavy wool or silk petticoats, a gown of the same, at least one kerchief about the neck, lined wool mitts, cap and possibly a kerchief tied about the ears, a hat or hood, the cloak added when going outside. A large wool bed jacket can also be put over the gown and often has longer sleeves. Most of these layers will be lined as well. That summer clothing I've weighed out at around 6-8 lbs including shoes. The winter I've had above 20 lbs before.