When to Apply for Full-time positions coming out of school?

Hi guys,
Im a senior at a non-target school graduating in May and was curious about applying for full-time positions. Is it best to apply now in the fall, or later on in the winter/spring?

Ive had a few interviews with private equity firms and smaller brokerage shops that are interviewing now on campus and currently waiting to hear back on, BUT i've also applied to many banks (UBS, Nomura and others) for leveraged finance/capital markets positions and they have gotten back to me asking for a phone interview.

However during 3 phone interviews now they have told me they are actually looking for immediate hires and to apply back in February when I am closer to graduation. Was just curious what you guys thought, I feel bedsides this private equity firm, most good places are asking me to apply later in the winter/spring time but I've heard that most recruiting gets wrapped up before Thanksgiving, I'm just very confused.
Thanks in advance,