yes, of course ! knowing myself , the first time i dive in UK i will need 20 UK divers around me !! so generally you would say you need more weight in colder water because of wetsuit ? also does the weight changes with depth ? as i go deeper i need more weight too ?
You'll need a thicker wetsuit (or a drysuit) in colder water, and neoprene floats, so all else being equal, you'll need more lead with a thicker wetsuit. Of course, if you change your gear (steel instead of aluminum tanks, a steel backplate), or change from salt to fresh water, that will also make a big difference. If your own weight changes significantly, that will make a difference too (fat floats).
You actually need less lead at depth, because the wetsuit will compress and be less buoyant. However, the water might be colder if you're diving deeper, and you might need a thicker wetsuit to stay warm on deeper dives, because the wetsuit will compress and not keep you as warm.
It's all explained in your OW book, but it takes practice too. Writing down what you wore for each dive, and how you felt with that gear configuration, will help a lot. I have 1 page in my log book for each dive, and about 1/4 of the page is data about the gear, water temperature, and environment. By the way, if you use the standard PADI log book, it has spaces to record all of the data, but you have to add whether you were happy with the gear.