Is one allowed to spray cologne on shabbos? Any rules against doing this?
As always, please cite your sources
The primary source is the in Gemara in Bietza 23a which discusses Molid Re'ech - creating a smell on an object.
Rashi (D'Ka Molid) there explains that it's a Rabbinic prohibition; it's similar to doing work.
This does not apply to food items, according to most Poskim - and according to how we Pasken.
The earlier Poskim argue if this applies to the body. For example, the Taz (511:8) disallowed it. However the Mishna Berura allows it. (This can be inferred from 327:1 that a healthy person can use Rose Water.)
There's some major discussion if it's allowed even if it will inevitably cause one's clothes to also smell good.
All this - with lots of sources - and more you can find on page 330 of Vol 3 in Sefer Orchot Shabbat (In Hebrew, by Rabbis Gelber and Rubin, Jerusalem 2009 ).
In short: If you spray it onto your body - but not enough that your clothes will smell of it - then everybody allows it.