It depends on what characters are trying to do. If the slimy floor is the obstacle, then it's there without fate points, but it's the narrative detail and not the aspect that matters. If the aspect describes something about that would make a task easier or more difficult, for example if characters were fighting on the slimy floor and it was really important to stay clean, then the aspect only exists when people pay fate points for it, and even then may only exist convincingly if a margin of success sufficient to give someone a consequence is achieved. This is because of how Fate Core integrates aspects mechanically-- while they can be used descriptively to justify outcomes whenever a player wishes, they only actually influence outcomes when points are spent. Furthermore, spending points results in a numeric modified applied to the roll; aspects don't completely modify how skills work or replace them with different skills-- stunts are for that.
This means that a Slimy Floor aspect is possibly not what you are looking for to model the increased difficulty and extreme lethality involved in the above cleanliness-based melee. While an aspect may be useful as an additional feature, other systemic changes (like changes to how consequences work in this contest, an additional Cleanliness stress track, a pervasive -2 fight modifier, etc) might be much more important to making the floor detail 'real'. What exactly is needed will depend on the situation, but I generally require in my Core games that every situation aspect has an associated stunt everybody in the area has, like: "slippery floor: you take a -1 to rolls where floor traction is important".