27 1 3/8 tires on 27 1 1/4 rims
Tires that are 27 x anything all have a bead seat diameter of 630 mm, so they should fit on the rim as the tire diameter is the same.  (Assuming of course your current tires (27 1 1/4) fit correctly). That leaves the following questions:


Are your rim width wide enough for the wider tire?  
Does your frame have sufficient clearance
If you have fenders, do your fenders have sufficient clearance.


The widths of the two sizes in question are 32 mm  and 35 mm respectively, which is a small change in width, so it is likely that if again if your current tires (27 1 1/4 tires) currently fit correctly, the slightly wider tires should be fine.

Finally, whether or not the Kenda K161 are appropriate depends on what you mean as "slippery".  If "slippery" means wet, then the tire compound matters most (bicycle tires are too narrow to hydroplane), look for soft tacky rubber. If "slippery" means compacted snow, then the lug pattern (see below) could help.  If "slippery" means black ice, few if any tires will be sufficient (maybe the Continental Top Winter Contact, but I have never used them). If "slippery" is actual ice, then studded tires are best.

Kenda K161