This is generally true, but like most things in nature, there are exceptions. There is no capacity to hold additional water once soils are saturated to the surface and infiltration is limited by the generally slow rate of groundwater flow. This produces saturation-dependent overland flow and greatly increases runoff.
Another effect is that cold conditions reduce vegetation growth, especially annual grasses. The lower groundcover promotes runoff.
However, under dry conditions some soil types can become hydrophobic, which also reduces infiltration and increases runoff. This can be due to coating of soil particles with organic substances as can occur in native forests in Australia due to eucalyptus and other oils. I believe this is a bit of an over-simplification because it does not consider the unsaturated flow dynamics that could impede infiltration without organic coatings.