Hey Anna,
Since you are in Texas (zone 8a) I would say you could use the tea in the fall/winter. Here in Cantonment, FL (zone 8b) the person I share a garden/hybridizing area with (their place) uses the tea year round, even in the winter. I choose not to use the tea just because there is soooo many daylilies around here to pour it around. I like the ease of throwing down lots of alfalfa pellets and I would think the worms get more benefit from them that way. I know the tea feeds the soil microbes so it really is a win-win no matter which way the alfalfa is used.