The Master Gardner handbook is currently under routine review for needed revisions for a pending new edition release. This statement may have been a generalized  over-simplification of the varying processes/conditions that influence herbicide efficacy, but overall, control via systemic herbicides is best during active plant growth. Active growth periods vary by plant species and its responses to environmental conditions, such as temperature, moisture availability, daylength, and stage of plant maturity. Sap flow follows a "source-to-sink" pathway (that is, from places it's generated/stored to places it's needed to support growth/metabolism), and carbohydrates generated by the foliage do feed the roots; hormones produced by actively-growing tips tend to trigger root growth (and vice versa). Therefore, it's not uncommon for root growth to coincide with shoot growth, and in periods of such activity the chemical should translocate into root tissues after absorption above-ground. Muddying efficacy are traits such as herbicide resistance, weathering effects after application, and external environmental triggers that happen to slow or halt plant growth after an application was made, resulting in limited control. Some research has indicated that glyphosate seems to have a limited window of time in which it can translocate after absorption, so if conditions suppress plant activity during this window, it is conceivable that this will reduce the success of the treatment.

As a generalization, yes, glyphosate should work to control weeds in active growth, regardless of time of year. (Though most active growth takes place in mild weather.) It's possible that with certain plant groups (perennials, deciduous shrubs/trees) this translocation effect is more substantial/efficient in autumn versus spring, though supporting research would need to be ascertained.

Miri