Keep the book sheltered
A notebook does not have to be waterproof to be useful outdoors, but ordinary paper needs shelter. Put the book in a closing pocket or reusable pouch between entries. Under a tree is not always dry: large drops can keep falling long after the rain has eased. Find a covered place before opening a page.
Graphite is a practical starting point for uncertain weather because it does not depend on water-based ink staying in place. That does not make the paper indestructible. Wet fibres can tear under pressure, so write lightly and avoid repeated erasing.
Capture less, more clearly
Cold hands make small lettering difficult. Write a few larger words, a time, and a rough sketch rather than trying to preserve a whole paragraph. Add the fuller account indoors while the scene is fresh. Mark the later addition so you can distinguish immediate observation from memory.
When conditions make stopping uncomfortable or unsafe, let the note wait. No page is worth losing your footing or standing in a cycle lane. A short recollection from shelter is better than a precise record gathered carelessly.
Dry before closing
If a book becomes damp, let it air in a dry, ventilated room. Do not put it directly on a heater. Separate a few pages gently if they are sticking, without pulling at fragile corners. Let it dry fully before packing it into a tight shelf.
Some wrinkling is a record of use rather than damage that needs correcting. If the writing remains legible and the binding is sound, keep working. For the next outing, a better pocket may be more useful than a more expensive notebook.