Does the slow effect last longer depending on the amount of frost damage dealt? If I choose to enchant a weapon with frost, can I get away with adding only 1 point of frost damage so I can maximize the number of charges added, or will slow also last only 1 second? Will it even have a slow effect at all on my weapon?
Based on the UESP wiki It appears that the length is based on the magnitude of the enchantment, which means that the two are tied together-- Note the last note of the comment section. I don't see anything in the formulae given differentiating duration from damage. I'd suggest reading over the wiki article then experimenting with a couple of iron daggers.
However, the elder scrolls wikia had a note stating that "For enchants that have two effects, e.g. Fiery Soul Trap, The second effect is constant and the number of charges is based on the first effect. This means that you can set it to one second soul trap and still keep the +10 fire damage. With a grand soul you can get over 2000 charges of +10 fire damage using Firey Soul Trap, but you would only be able to get around 50 charges if you used the Fire Damage enchant to get the same +10 Damage."
However, slow is one effect, so I'm not sure if this applies. Again, I suggest experimentation.