The difficulty depends on a variety of factors, like class, level and party composition, although the broodmother should be easy for any character without suicidal impulses.
The development of rogues and warriors is artificially delayed by level restrictions and padding feats while mages own the scene from the word go. However, extending a spellbook to the point where tougher nuts can be cracked efficiently by a soloing mage can take a long time indeed. Problematic points are: enemies protected by meat shields, clusters of elite and/or fire-proof enemies, melee bosses like alpha ogres and revenants, and ambushes with groups of enemies placed further apart than the Fireball AoE (i.e. requiring something like Sleep or Blood Wound).
Right out of Lothering a mage can ace the Broken Circle but the other quest lines all have their own special little headaches that require more than a core spellbook.
Honnleath has an ambush-style fight involving a bunch of rage demons, and this can be difficult without frost spells or some fire resistance.
RtO has a bossy ogre with some adds.
The Keep can be taxing for a soloing Warden early on because of the non-stop waves of enemies in the courtyard and at the rift. A mage before level 10 will probably lack the firepower and mana reserves to solo it on something like one or two lesser pots.
Denerim has mass ambush encounters, some of them with meat shields. However, the market area and The Pearl do not pose significant difficulties.
Haven has groups of elite ashwraiths and a trio of drakes, all of which are fire-proof. When fighting outside, Kolgrim is backed by a drake and a bunch of minor adds. Fighting him inside is easier but it requires CC with a large AoE (Sleep or Blood Wound) or a tank.
The Brecilian mission has a high concentration of revenants, and a bossy blood mage* with adds protected by meat shields.
Orzammar has the reception committee**, the informal training, the spider queen and the final assembly brouhaha where most AoE spells can only be used by Sith. Pairs of elite golems can be tricky for an early soloing mage. In two mass encounters you can easily lose kills if you don't have a capable team or a well-rounded spellbook.
Cadash Thaig has one mass encounter with kill stealage, and a bossy ogre at the end.
Redcliffe is dead easy if you're a Sith or if you care only about your own survival. It is the most difficult mission of all if you want to do your job and get all of the villagers through the fight.
The weight of these headaches will be different for different classes or different spell/ability progressions. Some things get a lot easier if you bring a team or gain a few levels by doing another mission first, others not so much.
*) The Mad Hatter is a bossy blood mage as well but the tactical situation makes him much easier to deal with than Zathrian.
**) Not to mention that the enemy scaling makes a Lothering-level team fight against bounty hunters who are level 9 and 10; this matters most in resistance checks where one level of difference is worth 10 attribute points in the 'defending' attribute group, not to mention that your attacking attribute (strength or spellpower) will be lower because of the levels you haven't taken yet. Jarvia's and the Deep Roads seem to scale normally enough.