For All Tours: your own water bottle, comfortable covered shoes, ID/Wallet for potential stops and purchases at local venues, backpack for layers. Most bikes have a bottle cage, but it's always good to have a small backpack.
For Tours In Warm Weather: covered athletic shoes and breathable pants or shorts that allow a good range of movement in your legs and fitted around the ankles (so it doesn't get caught in the bike chain). Sunglasses, sunscreen, and a sun hat for when you are off the bike is also a good idea. For hiking tours, be sure to bring shoes with tread. For certain tours, you may also want a swimsuit.
For Tours In Cold Weather: shoes with good tread as some walking over icy patches may be required. Hiking boots are perfect. Warm socks. Warm pants that allow good range of movement and layers like rain pants (for wind chill and puddles) or even snow pants can be helpful. Breathable, stretchy layers on top, such as a thermal or long sleeve athletic shirt, with another soft thermal layer on top, and a wind or rain jacket on top of that. Warm ski hat (with smooth top so it fits under helmet) and warm gloves, like ski gloves are a must for biking. You can also rent hats, gloves, thermal underwear (all good layers for winter riding), and more from Mountain Threads (https://mountainthreads.com/) and have it delivered to your accommodations if needed.