My question is the following:



> 
> Is there a small complex, perhaps analogous to the Chevalley-Eilenberg complex, computing the (co)homology of a restricted Lie algebra over a field of characteristic $p>0$?
> 
> 
> 


Even if the answer is no, I would appreciate any references dealing with such computations.



Computation of restricted Lie algebra (co)homology
That was a large part of the subject of my 1964 PhD thesis. 
While the motivation came from algebraic topology, the 
relevant algebra was published separately in the paper
<http://www.math.uchicago.edu/~may/PAPERS/3.pdf>.
It is very obvious from the case of abelian restricted
Lie algebras with zero restriction what the minimal
size of a $V(L)$-projective resolution of the ground field $k$
can be, where $L$ is a restricted Lie algebra with enveloping
algebra $V(L)$. Section 6 of that paper constructs a resolution
$X(L)$ of that minimal size for any $L$, using the theory of 
twisted tensor products. 


The serious part of the mathematics is to construct a 
coproduct on $X(L)$ suitable for computing 
$Ext\_{V(L)}^\*(k,k)$ as an algebra. In characteristic $2$,
the coproduct is coassociative and very explicit, as explained
in Remarks 10, op cit, and $X(L)$ embeds into the bar constuction
via a map of differential coalgebras. In char $p>2$, the price 
one pays for minimal size is that the coproduct is defined inductively 
and is not coassociative. The embedding into the bar construction
is then only compatible with coproducts up to homotopy. The paper
also gives a spectral sequence for computing the restricted Lie algebra 
cohomology from the cohomology of the underlying Lie algebra; that eases
calculations and minimizes the difficulty caused by the cited non-coassociativity.


