Can viruses pass through sweat pores?
'Pore' is a confusing term. Sweat is produced in sweat glands, and subsequently excreted through a duct, as indicated in the image below (sudoriferous ~).

In short, viruses cannot enter the body through these glands because the glands don't really open up into the body, but instead the inside of the sweat gland is lined with sweat-producing cells (fig 2 and 3).

A passive protection mechanism preventing infection is similar to the mechanism by which the bladder is guarded from infection through the urethra: even if some malignant agent were to enter the sweat duct, it is simply pushed out by the excreted sweat.



Figure one: Sweat glands in skin. Source: wikimedia commons.


(source: uwa.edu.au)  

Figure two: Slide of sweat gland. Tightly packed secretory cells dump sweat into the lumen through exocytosis (see fig 3). Source: University of Western Australia.



Figure three: Exocytosis. The lining of the sweat gland contains cells producing sweat through exocytosis. Viruses and other pathogens cannot simply enter these cells, and also cannot 'slip in between' the cells. Source: wikimedia commons.