While reactions between closed shell molecules generally involve prohibitive barriers in the gas phase, prior experimental and theoretical studies have demonstrated that some of these reactions are significantly enhanced when confined within an icy grain mantle and can occur efficiently at temperatures below 100 K with no additional energy processing. The archetypal case is the reaction of formaldehyde (H2CO) and ammonia (NH 3) to yield hydroxymethylamine (NH2CH2OH). In the present work we have characterized reactions involving methanol (CH 3OH), carbon dioxide (CO2), carbon monoxide (CO), and isocyanic acid (HNCO) in search of other favorable cases. Most of the emphasis is on CH3OH, which was investigated in the two-body reaction with one H2CO and the three-body reaction with two H2CO molecules. The addition of a second H2CO to the product of the reaction between CH3OH and H2CO was also considered as an alternative route to longer polyoxymethylene polymers of the -CH2O- form. The reaction between HNCO and NH3 was studied to determine if it can compete against the barrierless charge transfer process that yields OCN - and NH4+. Finally, the H2CO + NH3 reaction was revisited with additional benchmark calculations that confirm that little or no barrier is present when it occurs in ice.