Consider the role the person is playing in the document. Are they a reviewee (the person whose performance is being formally reveiwed), as opposed to a reviewer (the person who reviews and provides feedback)? Although most staff will ultimately experience both roles over a year, for the purposes of the policy, they are only playing one role at any one time.
If it's just unsolicited or sporadic feedback, provider of feedback and recipient of feedback might be the simplest answer. Afte the first mention, you can drop the 'of feedback'.
Employee probably feels cold because it emphasises the wrong thing - the employment relationship between the organisation and the worker, as opposed to the relationship between the person giving feedback and the person it's about.
Colleague may work, but can seem formal because it's used as a catch-all term so often. It means 'someone who works with you' and emphasises that you both work for the same company, it is probably fine for a form for feeding back on staff at a similar level, provided you can generally write "your colleague" rather than "the colleague" which undermines the collegiality. When used by very senior staff to refer to very junior staff it can feel condescending, however.
Peer means 'someone who is similar to you in status'. It is quite formal and in most cases in cases colleague would be fine as well. Typically peers are people who have a similar job title and one does not report to the other.
Member of staff or staff member is perfectly acceptable and is somewhat warmer than the other options but cumbersome to use, especially if you end up trying to use it in constructions like the other member of staff.