Sounds like the speed-sensitive power steering feature might be acting up.
Also:
- grabbing brake(s)
- bad wheel bearing(s)
- loose rack mounts
- failing rack/pinion
- failing flex-coupler
- contaminated/dirty fluid (ice?)
- blocked/pinched/deteriorated hose(s)
- loose steering wheel/column mounts
- worn suspension: ball joints/control arms/links/broken or cracked mounts
- combination of above