Skin wrinkles are generally caused by a breakdown of the collagen framework within the skin.
Collagen is a key part of your skin's structure. It forms a network of fibers within your skin that acts like a framework.
In young skin, the collagen framework is intact and the skin remains moisturized and elastic. Over time, the support structure weakens and the skin loses its elasticity. The skin begins to lose its tone as the collagen support wears down.
Wrinkles and other signs of skin ageing can be influenced by habits and behaviours during a person's life. Avoiding some risk factors for premature skin ageing can help keep skin looking younger for longer.
As well as smoking causing premature skin aging,
Wrinkles at the corners of the eyes (crow's feet) or between the eyebrows (frown lines) are thought to be caused by small muscle contractions. Over a lifetime, habitual facial expressions like frowning, smiling or squinting leave their mark on our skin.
The first link states that
Using your facial muscles -- smiling, frowning, or squinting, for instance -- is part of expressing yourself. That's normal, but it does stress the collagen in your skin. Over time, that stress adds up and contributes to facial lines and wrinkles.
To answer your question concerning hot and cold showers or baths, the processes within the body which help with homeostasis could have an effect on the collagen framework.
Vasoconstriction and vasodilation are the processes which take place to alter the amount of blood flow throught the capilliaries of the skin.
Blood vessels leading to the skin capillaries become narrower — they constrict — letting less blood flow through the skin and conserving heat in the body.
My question would be would vasoconstriction and vasodilation have such a big impact on the collagen framework? I cannot find any articles which answer this and therefore I would say that this is open to opinion. On the other hand, another aspect of bathing is that the skin wrinkles in baths, and in the shower if you're in there long enough.
The epidermis, or outer layer of the skin, is made up of cells called keratinocytes,
which form a very strong intracellular skeleton made up of a protein called keratin. These cells divide rapidly at the bottom of epidermis, pushing the higher cells upward. After migrating about halfway from the bottom of this layer to the top, the cells undergo a programmed death. The nucleus involutes, leaving alternating layers of the cell membrane, made of lipids, and the inside, made largely of water-loving keratin. The outer layer of the epidermis, called the stratum corneum, is thus composed of these alternating bands.
When hands are soaked in water, the keratin absorbs it and swells. The inside of the fingers, however, does not swell. As a result, there is relatively too much stratum corneum and it wrinkles, just like a gathered skirt. This bunching up occurs on fingers and toes because the epidermis is much thicker on the hands and feet than elsewhere on the body. (The hair and nails, which contain different types of keratin, also absorb some water. This is why the nails get softer after bathing or doing the dishes.)
This skin bunching happens in hot and cold water, and it can lead to damage to the collagen framework just like any other skin movement through frowning, smiling etc.