Foals can have very lateral movement for a while after their birth.
This type of lateral movement is not limited to gaited horses as non-gaited foals have been seen to exhibit this also.
Here are some of the reasons why foals go pacey, even those who have no easy
gaits in their background:
 Long legs, short body -- most creatures with this conformation do some
variety of stepping pace because that is the only way they can keep from
hitting themselves on a front leg with a hind (Camel, giraffe, some types
of dogs, cats, etc.).
 Long hind legs which put the hocks way behind the butt, preventing,
obviously, much lowering of the hindquarters or rounding in the body.
 Short upright neck, with no withers. Foals are always proportioned this
way, and the lack of withers pretty much precludes stretching the cervical
ligaments over them. These last two things mean that he is by nature stuck
in a somewhat hollow frame for now and the foreseeable future. This is part
of it, but since the foal will stay in this relative shape for a while, it is not all of it.
So, on to the "softer" systems that may be causing this:
 Foals have relatively weak abdominals -- a little pot bellied.
 A foal has an immature neurological system, that has yet to settle into
specific pathways and so doesn't play as much as a role in what he does as
the terrain he is negotiating.
 And above all, he has the flexibility of extreme youth -- he can tie
himself in knots, as can just about all babies .. so he has a lot of
looseness in his back muscles that he won't have as he matures. This is the
first "baby" thing that he will grow out of, even when his proportions stay
what they are.
A Standardbred breeder of trotters adds that her foals do the same, and after about a month they go to trotting.
Lee Ziegler, noted gaited horse expert, clinician, judge, and author of Gaits Without Gimmicks, who wrote the above, also adds her feeling that since Standardbreds also come in "pacing" models, that some may feel the gene is hidden in these foals, but it is doubtful since the phenomenon also occurs in Thoroughbred, Warmblood, and other breed foals.
I've been watching my babies as they grow (quickly), making mental notes
about their gaits as they change.
Have any of you other "grand-mares" been noticing what gaits your babies are
doing at liberty?
About all of my foals mostly paced their first couple of days. I think
that's pretty normal - I was an ad in a major magazine recently (don't
remember the product) and a mare (appeared QH) was trotting along with her
new foal at her side - with the foal doing a pace, or maybe a step pace.
Landi trotted a little his first day, but now I see him step-pace too. He
and Tifa have nice little flat walks - in fact I think they all do. Not
sure about Isak's gaits yet - he's always harassing a sibling, sleeping or
galloping, with little time to show off his intermediate gait(s)! I've seen
Tifa do a good bit of running walk - in fact, that seems to be her
preference. Kola was a little pacey at first like the others, but now I see
her trot a good bit too, and I've caught a picture or two of her
Interestingly, Landi also had a lot of what folks call "lift" - I call it
knee action - his first few days. He trotted around like a little hackney
pony! I've seen folks send in pics of their newborn foals lifting their
legs, as signs of "talent" - I'm sure what we saw in Landi was simply the
loosey-goosey joints of a newborn. I'm not seeing it any more. Sina has
virtually no lift - she's a very efficient mover. I'm not a big fan of knee
action, since it's a waste of energy for the trail/pleasure horse. I do
believe Landi may have his mom's to-die-for canter, but maybe it's too soon
to know for sure.
It's funny that we think it's so special when we manage to get a horse to do
a flying lead change under saddle. The foals could all do them the day they
were born. I love watching the babies. It just amazes me how athletic they
are so soon after they are born. Such fun!