Depends on the species. This really isn't the time of year to do any pruning. The sap is really pumping. Best to do it when the tree is dormant. Coniferous trees can generally be pruned any time, if necessary, but deciduos trees are prone to poor healing and disease if you prune when not dormant.
Dead branches can be removed any time. Just be certain they are dead.
I really have no clue what kind of tree it is... except it's definitely deciduous and has yellow fern-frondy kinda leaves? I really ought to google it and see if I can find it...
Took another look outside and the dead branches (no yellow fern-frondy kinda leaves) may be out of reach even with my ladder. The tree itself is on my side of the sidewalk, but some of the (live) branches are close to the power lines... so I may just call LondonHydro and see if they'll come and prune those branches and maybe convince the guy to hack off the dead ones while he's up there.