Since in the geometric sequence $\{a_n\}$ with each term being positive, we have $a_2a_5a_8=8$,
then $(a_5)^3=8$,
thus $a_5=2$,
therefore $\log_2a_4+\log_2a_6=\log_2(a_4a_6)=\log_2((a_5)^2)=2$
Hence, the answer is $\boxed{\text{B}}$.

Analysis: By utilizing the condition that in the geometric sequence $\{a_n\}$ with each term being positive, $a_2a_5a_8=8$, we find $a_5=2$. Then, by applying the properties of logarithms, we can draw the conclusion.