It's absolutely fine to give ponies a month or so off at this time of year - mine's been off since late November and won't be back in until after Christmas now, dark, cold etc. make it challenging to ride, so plenty of people do 'rough' off over the winter esp if they have good turnout, I think it's actually good for them to get a break and some prolonged field time, and personally I'd rather do that in winter than in summer when there's more fun to be had.
So I think where you went 'wrong' (not badly, but a bit) was not in giving the pony the month off, it was expecting to be able to get back on and ride just like normal without proper prep. Some horses can be a bit wild this time of year anyway, wind and cold air can really affect certain types, and as this is your first winter with this pony you weren't to know whether she's one of the ones who are particularly bad with it, plus your DD probably wasn't on her absolute A game either not having ridden for a month. So with those factors I would probably have done a few things:
-Built up to riding with at least a few days of groundwork, in hand or on the lunge or long rein first, partially to check how her fitness was affected by the month off and also to assess freshness lunacy levels so as to gauge when best to get back on.
-Before 1st ride would probably have lunged for 5-10 mins first to let any 'hoolies' out and get rid of the worst of the freshness, as they can have a buck and a plunge on the lunge without hurting anyone. If the horse seemed just too fresh or spooky on the day I'd planned to ride (e.g. if it was a particularly windy day or something spooky was worrying them or the arena was very busy) discretion can be the better part of valour so leave it for another day if in doubt.
-Having decided to ride I would stick a neck strap on and be well prepared to grab it if needed. Keep it low key and short for a first session (10-15 mins fine), walk and maybe a bit of trot only, lots of changes of directions and circles and transitions as others have said, insisting on the horse paying attention and staying in front of the leg. Almost certainly no cantering until I'd been riding back at least a couple of days in a row and the horse feels settled and calm. If the horse is a known bucker/spooker I would be well prepared for it in my riding (concentrating at all times!) by keeping my weight and centre of gravity well back in the saddle, heels down (maybe shorten stirrups a few holes for better balance if lower leg unstable), firm short rein contact (not tight or pulling but a good hold of their mouth) and ensure the pony isn't allowed to tip onto the forehand or take her poll down behind the vertical as this is when they can get a really good unseating buck or spin in. And like I say being not ashamed to grab the neckstrap or a handful of mane in the event of an 'emergency' gives you a much better chance of staying on!
-I try and schedule a saddle fit check, physio/back lady visit and dentist asap after a break - they can change shape a lot after just a few weeks in the field and if the pony has suddenly started bucking that to me could indicate a saddle pinching somewhere or possibly a sore back.
So I'd keep on riding but build up to it with some prep first, if a more experienced rider needs to school her for a few days to get the fizz out then that would be fine, perhaps also you could book an instructor to supervise DD's next ride as you don't want her losing confidence by getting chucked off too much, but equally this can be a great learning opportunity on what to do with a fresh horse!