Hello Catherine,

Thanks for your questions. This small willow isn't one that is commonly pruned often to reduce size. That said, it will certainly tolerate pruning well, as most willows do! I know it certainly does grow larger than often advertised by nurseries.

RE pruning the artic blue willow to keep it compact: 

If you would like to keep it smaller overall, it does tolerate pruning like a boxwood, where you can shape it by shearing it or cutting each tip of individual stems. The same cautions apply to this as with shearing other plants. You won't want to do it more than once a year and avoid pruning in autumn the because the new growth may not have time to harden-off ahead of colder temperatures and could be damaged. 

Because willows are generally so vigorous in their growth response to pruning, if taking this approach - I would recommend every other year rather than annually. I haven't seen this one sheared/shaped/hedged often...but I did find an image on this nursery's site of what it might look like with years of repeated shearing: Dwarf Blue Arctic Willow for Sale Online - The Greenhouse (thegreenhousepnw.com) 

Another pruning approach is to reduce size over time is to nearly coppice it by cutting the main stems all back to about 6 in-1ft off the ground in very early spring. Willows respond to this technique very well. While I haven't seen it done often with this species, it is often done with larger willows. 

Both of these techniques are often done with a larger shrubby willow - Salix integra 'Hakura Nishiki' - the tri-color willow. If you google that plant name and the word 'pruning' you will find many different images that will give you examples of both of these options to help you decide how you want to proceed to achieve the particular look you are going for.

Whichever approach you choose, I would wait until the plant has been in the ground for a couple years so that its roots are established in its new location.

RE 'invasiveness' of roots: 

I am assuming that you mean 'invasiveness' as aggressive or i'nvading drain pipes and etc. Like other willows they have dense fibrous roots but they willl not produce the large roots of a tree like a weeping willow. That said, roots are opportunistic and if they are growing near a cracked drainpipe or something, they will find the water. 

Hope this helps and Go Spartans!