It can be done, just did it last night, it was around 15F.
But there are a few tenants that have to be observed:
Don't use too many layers, no matter how "breathable" they are, they won't breathe with too many. Usually more than 2 is too many, unless you are real cold and need to warm up, but sustained exertion in more than 2 layers is often a contributor to getting damp.
Waterproof membranes are not breathable. No matter what they claim, it just doesn't work for high exertion sports like mountain biking where you are often not moving fast, but outputting high (climb). Avoid waterproof membranes unless absolutely necessary for conditions, and even then you can still expect to get damp either due to this, or the fact that they tend to get overwhelmed in anything more than relatively light precip. They do help a bit trapping heat and creating a seperate warmer damp layer underneath, but you gotta play that one careful, because that can make you ultra-cold if your exertion falls way off. When it gets real cold, like down in to the 0F range and less, then the waterproof stuff can start to become more useful again, since it's cold enough to keep you from sweating bad and it helps to trap heat.
XC ski clothing has most of this figured out, it's a good template to use. XC ski pants can usually deal with a pretty wide range of temps, from nearly 50 down to the low positive F temps. This stuff often has a wind-proof front layer and the back layer is totally breathable stretch material.
You gotta manage it while you ride. Unzip the jacket, take it off and tie it around your waist if it's that warm, roll up your sleaves, put them down, etc. Stop and manage it. This step can often be a lot harder than it sounds, as in it's a mental challenge, but it makes a big positive difference when you are doing it.
Most people wear too much gear so that they are "comfortable" when they start, but 15 minutes later or on a climb, they are just pouring sweat. Gotta start colder than you think. Always bring an extra layer though as a bail out. Packable jackets are amazing. They even make relatively packable pants, size-zip stuff that can be put on relatively easily with the full side zips, if you are running a frame bag, it gives you the option to do stuff like this, but there are still ways to do it, like revelate feed-bags, etc.
It really depends on the temp range and the appropriate clothes and not over-doing it. Sometimes it's shorts and yoga pants or base-layer pants, sometimes it's the XC ski pants. Sometimes it's backcountry ski pants or in extreme situations, mountaineering pants, but within each of these options, you want the least amount you can get away with, realizing once you start exercising and your core temp goes up that you'll be warm. For the tops, as it gets colder we will often put on a down puffy over our outer jacket if it gets cold enough, down packs to a small size great, but there's also the packable jackets I was talking about above for warmer climates. It helps to have a few different thicknesses of soft-shell jackets, like a super light one for warmer conditions, a thicker one for colder conditions. Same thing with base layers. IME, having a few different thickness base layer options and the right features on the base layer is far more important than whether it is made out of synthetic or sheep's butt hair. And in that same vein, synthetic breathes better and dries faster, sometimes while you are riding. When you get it home, make sure to dry it out immediately, even if you are dry, you often still carry a little dampness, don't throw it in a basket with other stuff on top so it can fester. It will work great as long as you keep it dry.
Try not to wear a pack, that will generally cause more sweating. A hip pack is a little better, but no pack is best.
So in summary, the #1 thing I see is people wearing too much clothes, either too thick, or too many layers. This may be related to people not knowing how to bring extra clothes with them. The 2nd one is usually people wearing "waterproof" stuff. The third is not adjusting their gear, opening up, unzipping, taking on/off, etc.
It would help to know what kind of temperature range we are talking about though.
