Winter Witch PrC Learning New Spells

[Velisruna]

So I was looking at the winter witch PrC from Paths of Prestige and I was wondering if learned new spells at each level. I understand most prestige classes don't give new spells to prepared casters but in the Winter Witch class it says

Winter Witchcraft wrote:

Levels of the winter witch prestige class stack with witch levels for determining when she learns new hexes, the effect of her hexes and other witch class abilities (including archetype abilities), the abilities of her witch’s familiar, and the level at which she can select major hexes or grand hexes.

and the witch is different from most classes where the witch itself doesn't learn new spells, her familiar does. For the witch class, learning new spells isn't even mentioned in the spell casting ability, it is part of the familiar ability and is detailed further in the witch's familiar text. My question would be is learning spells treated as an ability of the familiar or is it still the witch learning the spells?

For Reference:

Witch's Spells:

Spells wrote:

A witch casts arcane spells drawn from the witch spell list (see pages 70–71). A witch must choose and prepare her spells ahead of time.

To learn or cast a spell, a witch must have an Intelligence score equal to at least 10 + the spell level. The Difficulty Class for a saving throw against a witch’s spell is 10 + the spell level + the witch’s Intelligence modifier.
A witch can cast only a certain number of spells of each spell level per day. Her base daily spell allotment is given on Table 2–10. In addition, she receives bonus spells per day if she has a high Intelligence score (see Table 1–3 of the Pathfinder RPG Core Rulebook).
A witch may know any number of spells. She must choose and prepare her spells ahead of time by getting 8 hours of sleep and spending 1 hour communing with her familiar. While communing, the witch decides which spells to prepare.

Witch's Familiar:

Quote:

At 1st level, a witch forms a close bond with a familiar, a creature that teaches her magic and helps to guide her along her path. Familiars also aid a witch by granting her skill bonuses, additional spells, and help with some types of magic. This functions like the wizard’s arcane bond class feature, except as noted in The Witch's Familiar section. A witch must commune with her familiar each day to prepare her spells. Familiars store all of the spells that a witch knows, and a witch cannot prepare a spell that is not stored by her familiar. A witch’s familiar begins play storing all of the 0-level witch spells plus three 1stlevel spells of the witch’s choice. The witch also selects a number of additional 1st-level spells equal to her Intelligence modifier to store in her familiar. At each new witch level, she adds two new spells of any spell level or levels that she can cast (based on her new witch level) to her familiar. A witch can also add additional spells to her familiar through a special ritual (see sidebar).

Store Spells:

wrote:

Starting at 1st level, a witch’s familiar stores all of the spells that the witch knows. This does not allow the familiar to cast these spells or use spell-trigger or spell completion magic items. Starting at 2nd level, and every two levels thereafter, a witch’s familiar adds new bonus spells to the witch’s spell list based on her patron. These spells are automatically stored by the familiar and can be prepared as normal once they are gained.

Winter Witch Spells per Day:

wrote:

At the indicated levels, a winter witch gains new spells per day and patron spells as if she had also gained a level in the witch class. She does not, however, gain other benefits a character of that class would have gained except for additional spells per day and an increased effective level of spellcasting.

Winter Witchcraft:

wrote:

Winter Witchcraft: Levels of the winter witch prestige class stack with witch levels for determining when she learns new hexes, the effect of her hexes and other witch class abilities (including archetype abilities), the abilities of her witch’s familiar, and the level at which she can select major hexes or grand hexes.

Adding Spells to a Witch's Familiar:

Spells Gained at a New Level wrote:

A witch’s familiar learns a certain amount of lore and magic as the witch adventures. Whenever a witch gains a level, she may add two spells from the witch spell list to her familiar. The two free spells must be of spell levels she can cast.

[Matthew Morris]

It's kind of a grey area. I know that wizards don't gain spells from prestige class, but since the text on a wtich's spells are in the familiar, and the familiar 'levels up' with the prestige class, I'm prone to say yes. It's also how I read it for my seeker witch.