I don't think in Houston there is any price advantage to resurface during a certain time of year. The summer is crazy busy, so you might deal with more delays. Weather is usually responsible for most delays. Someone else will have to answer if outdoor temps have any bearing. My pool was plastered in July of 2015, and it was extremely hot. My surface still looks great.
I've heard many of the regular crews (more experienced) take time off for a few weeks before and after Christmas. I don't know this for a fact.
I used a pool builder, so I can't say how it works otherwise. If I needed to resurface, I would go directly to the plaster companies if they will work with you - cut out the middleman.
You didn't say what surface you currently have on the pool.
Suz
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Oops.... I just saw in your signature, you have plaster.