I'm going to disagree with the others: Now is a good time to buy as lots of people will be selling and fewer looking. There's lots around at the minute, prices are low, and there's still time to get settled and do a bit before winter really kicks in. And the baptism of fire which is the first winter won't do her any harm. Depending on how you manage them (and their temperament) not all horses are difficult in winter, and on working livery will have enough work to keep it sensible.
I think it's best to write down what you want in a horse. Start with an honest appraisal of your dd's riding: strengths, areas where she's making progress, areas where she's still got a lot to learn. Get her to set out what she wants to do with the horse now and in the future. Consider whether she needs a schoolmaster or whether she could bring something on. Since it's going to working livery also include the requirements of the college. And take into account anything that may affect her confidence (eg, can sit a buck but spinning is terrifying, that sort of thing) This should help your dd get a view of what she's looking for in terms of size, style, ability, age etc. Then work out her budget.
Then it's time for a list: three columns 1) Totally essential 2) Would really like 3) Could compromise.
From this make a list of questions to ask when you phone about potential horses, and start looking! Try Horsemart, Preloved etc, Pony Club website, local tack and feed shops etc.
And keep us posted, we like vicaious horse shopping!