We have two types of explanation here: one physical, one chemical. It is likely that chemistry is responsible for the greater effect.
The sun would be fairly low in the winter sky, its rays shining almost directly on, and perpendicular to, the vertical plane of the lenses.
In the tropics, the sun could be almost directly overhead, and if walking around, the sun’s rays would strike the glasses edge-on. A sliver of radiant energy would be all that each lens would receive, thus reducing their shading reaction.
One of the little details opticians fail to mention about photo-chromic glasses is that they do not work as well when hot. Particles of silver halide trapped inside the glass are normally transparent, but when struck by ultraviolet light, they disassociate into halogen and metallic silver, which darkens the lenses.
As both components are trapped inside the glass, they will recombine when UV light is removed, when you go indoors, becoming transparent again.
The recombination reaction, like many others, speeds up as the temperature rises. As the darkness of the glasses at any moment is a balance between UV light-induced disassociation and the temperature-sensitive re-association, it takes much more UV to reach a given level of darkening in a warm climate.
Photochromic materials are sensitive to temperature and darken more when they are colder. My sunglasses turn really dark on an overcast day but change little in the midday sun of Florida. This is fine for skiers but not much use to sun-lovers.
Many photochromic lenses react almost entirely to UV radiation rather than to visible light, so they don’t darken properly inside a car.
The response of photochromic lenses to light is affected by temperature. Lower temperatures change the kinetics of the photochemical reaction so the reverse reaction, lens lightening, is delayed.
Photochromic lenses become much darker at lower temperatures. Living in the American Midwest provides me with perfect experimental conditions to test the temperature effects. With summer temperatures around 30 °C my photo-chromic lenses respond with a bluish-grey tint, whereas in deep winter, when it’s cold, they quickly become very dark.
The darker lens tint on sunny winter days is especially beneficial against strong snow-dazzle.
However, this heavy darkening is disconcerting when going indoors on a sunny day because it takes about 10 minutes for the lenses to return to normal.