The only way to significantly reduce caffeine content is to use decaffeinated tea or "herbal teas." I know it's probably not the ideal solution, given the limitations on variety and flavor.
There are various claims about which types of tea have more or less caffeine, but the reality is that there's a huge amount of variation in individual tea varieties and blends. Caffeine content has to do with how and where the tea leaves are grown, more than the way the tea is processed afterward (and it's the processing that determines whether a tea is black or green or white or whatever).
For example, this study notes, based on 20 different commercial teas:
Caffeine concentration in white, green, and black teas ranged from 14
to 61 mg per serving (6 or 8 oz) with no observable trend in caffeine
concentration due to the variety of tea.
Each sample was brewed for 1, 3, and 5 minute times, so most of the lower numbers resulted from the 1 minute infusions, while the high numbers came from 5 minutes.
Granted, this is a small sample, but you can find other similar studies that come to the same conclusions. (This study measured caffeine in 4 different ways and found the white tea sample to have the highest caffeine of all.)
I believe the idea that green and white teas have less caffeine comes from the fact that such teas are often brewed at lower water temperatures (steaming rather than a full boil), which will in fact reduce caffeine content somewhat. But if you brew all the teas at the same temperatures, you'll find little consistent differences among tea types.
Caffeine concentration does become greater with longer brewing times, but if you brew the tea for a shorter time, you're likely need to use more tea leaves to create sufficient flavor, which can negate any reduced caffeine effect from the shorter brew.
A similar thing can happen with temperature. Yes, caffeine will dissolve more slowly by brewing at a colder temperature (see here for a detailed experiment showing the rates), but so will many other flavor components. You'll obviously need to steep cold-brewed tea longer, and that longer steep may counteract the fact that caffeine dissolves more slowly. Whether you can end up with a cold-brewed tea that tastes like what you want with a lower caffeine content will likely depend on your exact process and your exact tea leaves.
In any case, if you're actually trying to reduce your caffeine consumption significantly, I'd have to recommend decaf or herbal teas. Some tea companies may publish statistics on how much caffeine their "regular" tea contains, but it's hard to say how reliable these are, how consistent they could be from year-to-year, or how they would be impacted by different brewing methods. And short of having that sort of information on brands, the only way to know whether switching your tea/method has an impact would be a lab test.