The Wings of Flying seem to be exactly what you're after. The flavor text of the spell states they turn into bat or bird wings, however, there is no reason they couldn't be formed out of ice as there wouldn't be any mechanical difference. You could just ask your GM to have the cloak be a light blue and transform into ice wings instead.
I could not find any other ways to get wings with actual flight for cheaper however if your GM allows the creation of unique magic items then you could create a similar item that uses the Glide spell. The cost for it to be a command word item at the minimum caster level would be 21600, to craft it yourself it would cost 10800 if you take the right feats.
Here is my math to calculate the cost.
Spell level assuming a wizard is crafting the item 2.
Lowest caster level possible is 3rd level.
The calculation for a command word magic item is Spell level * Caster level * 1800
2*3*1800=10800, double that if you outright buy the item cause the cost doubles to purchase.
If you are just after the look then an item with an illusion on it would also work and would be much cheaper as you could just use the Silent Illusion spell. A first level spell so the cost would be much cheaper, at only 1800 gold due to it only being a first level spell with 1 caster level needed. I would say this is reasonable cause there isn't really a mechanical benefit to this spell as all you get is a pair of illusory wings until you can get wings.