I have no bias but every spring it seems the leaf blown trails are the 1st to be ready to ride and in the better shape then the non-blown ones.
That makes sense, and it would fall under my spot treatment philosophy. Early in the spring, the wind probably plays more of a role in drying things out than during other times of the year, so getting wet leaves off the trail that are still covering parts of it would help.
Riding the trail when it's frozen helps crush out some of that frost heaved soil and seems to help pack it back down somewhat.
I would counter that in your video, you are drawing spurious conclusions based on what you think you are seeing. You are comparing sites with different positions on the hillside, and other differences that govern the behavior of soil moisture far more than frost heave. You have drawn these conclusions with no testing or statistical analysis to support them.
While it is generally correct that leaf litter dissipates the energy of rainfall and reduces soil displacement, you are not controlling for soil compaction. The soil on trail tread is heavily compacted, while the soil throughout the rest of the forest is generally not. We WANT compacted soil on trail tread. It makes for an enjoyable riding experience, and keeps the trail durable. Root exposure on trails has more to do with that compacted soil than with erosion. Those roots were sitting at the surface already, and became more exposed as the soil compacted.
The problems you are seeing are exacerbated by the fact that the trails in your video are "built" (I say that loosely) on very low-relief trail. Soil compaction creates the cupping of the trail that indytrekracer mentioned. That is what allowed for the soil displacement you illustrated in your video. The coverage of that soil on the bridge suggests that most of that soil displacement occurred in one or more high energy events. Heavy rainfall, where the soil's infiltration capacity was exceeded by the precipitation rate. That causes surface runoff. With proper trail design, we want surface runoff to flow off the SIDE of the trail, not down its length. This allows that surface runoff to flow into areas with leaf litter and downfall to reduce the energy of the flow, it allows that water to go to places where there is higher infiltration capacity (uncompacted soils underneath leaf litter).
On to your discussion about the leaf litter preventing freeze/thaw cycles. You are correct about one thing, that the leaf litter serves as insulation, reducing how frequently the soil is frozen. However, you have drawn the incorrect conclusion based on this observation. That soil under the leaves never froze. The reason it's not muddy is because it is higher on the hill than the muddy portion of the trail you illustrated. You shouldn't be out riding or hiking the trail when it just squeaks above freezing and begins to thaw out. When the soil sticks to your boots or to your tires, you're damaging the trail. Time your visits to the trail such that you're using them when the trail is still frozen. That means early in the morning and late at night. No mud.
Deep snow serves the same insulating function as leaves. Ever been on a snowy trail and your tire or boot tracks turn brown, even though it is well below freezing and the sun is not shining on the trail? It's actually better for riding conditions if the snow is shallow and the trail is frozen solid. During the cold season, appropriate riding conditions occur in a pretty narrow range. Visit the trails when the conditions are appropriate. Stay off when they are not.
The criteria begin to change in the springtime when two things occur: First, when the worms start coming out. They start becoming active when the freeze/thaw cycles have really dissipated and you start having warmer days (that help dry the trails out). Whether the trails are ready to ride depends heavily on local conditions. Recent precipitation, soil type, and topography make big differences. The next thing to affect trail conditions may seem odd, but leaf out makes quite a difference. When the trees begin leafing out, that means they're pulling up soil moisture. This helps wet soil to dry out faster.
None of these factors have anything to do with dead leaves on the trails. However, as irishpitbull mentions, in the springtime, trail tread exposed to the air may dry out faster. In part, this has to do with allowing air to circulate around the soil. As the wind blows over, it will help moisture evaporate more quickly from the surface of the trail. It also affects the sun exposure to the trail tread. Warm sun on that soil also helps accelerate evaporation. The insulation of the leaf litter on the trail will prevent those two factors from affecting the evaporation of the moisture on the trail tread.
In some places, that won't be a big deal. The trails see such low traffic that the small amount of moisture won't affect much and they'll have plenty of time to dry. Spots high on the hillside, on south facing slopes, soils with high infiltration rates (sandy or rocky soils), or areas exposed to a lot more wind or sun have factors that help dry the trail tread, so some leaf litter won't be a big deal. However, some spots need it. Deep valleys oriented perpendicular to the prevailing winds will tend to be sheltered and need all the help they can get. Trails on northern slopes won't get much sun exposure, if any at all, and will need all the help they can get. Areas with difficult drainage issues should have the leaves removed, as those leaves not only provide insulation and prevent evaporation, but they act as sponges as they decompose and keep keep the trail wetter longer. This is great for forest plants, but not for forest trails.