This is a great question - yes, this sort of approach can be applied to forecasts on shorter timescales, including monthly forecasts.  The skill from the trend, however, diminishes as we move to shorter timescales because the noise of random weather variability is larger on shorter timescales, drowning out more of the signal from the trend.  In other words, more of the noise gets averaged out on seasonal timescales than on monthly timescales.  Therefore, we could apply this technique to monthly forecasts, but we wouldn't expect as much skill attributed to the trend.