If by smaller you mean (smallest to largest due to e- cloud size) F- <Cl- <Br- < I-
-Weak bases (ie I-) react weakly with your protic solvents (alcohols and waters).. this is a good thing because you want them to be attacking an electron deficient species and being more nucleophilic rather than forming interactions with the solvents
- F- is a stronger base than I-. (you can think pkas here, polarizability, the fact the HI is a strong acid) and is more willing to pluck a proton (H+) than an I-. In general F- does not like to be by itself and will react more strongly with the protic solvents (the dudes who got H's) and the protic solvent shields the F- and stabilizes his charge to make him happier. The species under attack can dodge the bullet here.
Now for the distinction: in aprotic solvents (no Hs to pluck), base strength and nucleophilic strength are on the same team. This means that F- wont be interacting with the aprotic solvent because they wont make him happy and wants his charged satisfied more than the I- does (because hes a big boy and doesnt need to hold hands with anyone). This is how F-, the small guy, becomes a stronger nucleophile in an aprotic solvent