Like MtoA, Yeti exports UV coordinates in the uparamcoord and vparamcoord parameters, and you use these to map textures in the aiHair shader with the Uparam and Vparam extra attributes.

For example, if you plug a texture into the Rootcolor and tipcolor

then you can use uparamcoord and vparamcoord to map that texture onto the hair:

Tip If you enable Expand Procedurals and export an ASS file, you can see what parametes Yeti exports:
### created by pgYetiMayaShape
curves
{
name pgYetiMayaShape_|pgYetiMaya|pgYetiMayaShape|scatter01_pSphereShape1_grow01
num_points 621 1 b85UINT
# ...
points 4347 1 b85POINT
# ...
basis "catmull-rom"
mode "ribbon"
min_pixel_width 0
visibility 255
self_shadows on
matrix
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
shader "initialShadingGroup"
opaque on
id -1230660816
declare curve_id uniform UINT
curve_id 621 1 b85UINT
# ...
declare uparamcoord uniform FLOAT
uparamcoord 621 1 b85FLOAT
# ...
declare vparamcoord uniform FLOAT
vparamcoord 621 1 b85FLOAT
# ...
declare surf_s uniform FLOAT
surf_s 621 1 b85FLOAT
# ...
declare surf_t uniform FLOAT
surf_t 621 1 b85FLOAT
# ...
declare length uniform FLOAT
length 621 1 b85FLOAT
# ...
declare fur_id uniform FLOAT
fur_id 621 1 b85FLOAT
# ...
declare surf_n uniform VECTOR
surf_n 621 1 b85VECTOR
# ...
declare filename constant STRING
filename "C:/Users/StephenBlair/Documents/maya/projects/Support//yeti/tmp/yeti_combExample_pgYetiMayaShape_1886244453_1.fur"
declare mtoa_shading_groups constant ARRAY NODE
mtoa_shading_groups "initialShadingGroup"
declare frame constant INT
frame 1
declare verbosity constant INT
verbosity 1
declare density constant FLOAT
density 10
declare width constant FLOAT
width 1
declare threads constant INT
threads 0
declare min_pixel_width constant FLOAT
min_pixel_width 0
declare mode constant INT
mode 0
declare imageSearchPath constant STRING
imageSearchPath ""
declare samples constant ARRAY FLOAT
samples 1
}