Technically, no.
A witch's familiar begins play storing all of the 0-level witch spells plus three 1st-level 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.
You get a bonus set of 1st level spells. Come 2nd level, you can take the level 0 spell for free. However, I would talk to your GM. I see no problem with adding a cantrip to your familiar in place of a 1st level spell.
Huh? The Winter Witch archetype adds Ray of Frost to the witch spell list. Witch familiar's know all 0-level spells. Therefore, a Winter Witch can prepare Ray of Frost in one of the 0-level spell slots.
If your question is whether you can prepare an at-will 0-level spell using a 1st level slot, you should make it clearer. I would think the answer is already on the board that a search check would find.
cheers
The Winter Witch known all 0-level spells except Ray of Frost.
No. You are misunderstanding the text. Jubal is correct. Let me try to clarify.
A winter witch adds ray of frost to her spell list, but does not automatically learn this cantrip.
That means your familiar and by extension the witch knows it (because the familiar knows all 0 lvl spells available to the witch) but the winter witch still needs to select it in one of her 0-level cantrip slots to be able to cast it, just as normal.
As for PFS. It is legal for a Winter Witch to have Ray of Frost as a cantrip.
If we assume that "learn" means "to feed it to your familiar and so gain knowledge of the spell so that you can prepare it" then the answer is no. if we keep being pedantic:
A witch’s familiar begins play storing all of the 0-level witch spells plus three 1st level 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.
So by RAW you can only add it using the special ritual (e.g. buy a scroll, feed it to your familiar or learn it from another witch) or wait till level 2.
However this restriction is ludicrous. It's a cantrip for crying out loud. I would completely allow this as a freebie. I find it really hard to believe that it is so difficult for a winter witch to learn this cantrip but be given free wintery patron spells.
Take 10? Its easy to have a +11 at level 1 with an intellect based caster.
Can't take 10 as there is a penalty for failing.
Huh? Last time I checked, 'penalty for failing' precluded take 20 only.
I was hoping to just dump a 1st-level spell, but I figured I'd have to go the scroll route... Lets hope I don't bugger the skill check.
Take a race that has the favored class bonus of 'Add one spell from the witch spell list to the witch’s familiar. This spell must be at least one level below the highest spell level she can cast'. Problem solved.