  The forward Drell--Yan process in $pp$ scattering at the LHC at $\sqrt{S}=14$
TeV is considered. We analyze the Drell--Yan structure functions assuming the
dominance of a Compton-like emission of a virtual photon from a fast quark
scattering off the small $x$ gluons. The color dipole framework is applied to
perform quantitatively the twist decomposition of all the Drell--Yan structure
functions. Two models of the color dipole scattering are applied: the
Golec-Biernat--W\"{u}sthoff model and the dipole cross section obtained from
the Balitsky--Fadin--Kuraev--Lipatov evolution equation. The two models have
essentially different higher twist content and the gluon transverse momentum
distribution and lead to different significant effects beyond the collinear
leading twist description. It is found that the gluon transverse momentum
effects are significant in the Drell--Yan structure functions for all
Drell--Yan pair masses $M$, and the higher twist effects become important for
$M \lesssim 10$ GeV. It is found that the structure function $W_{TT}$ related
to the $A_2$ angular coefficient and the Lam--Tung observable $A_0 -A_2$ are
particularly sensitive to the gluon $k_T$ effects and to the higher twist
effects. A procedure is suggested how to disentangle the higher twist effects
from the gluon transverse momentum effects.
