Horses certainly were important to the Anglo-Saxons but not necessarily for the reasons they were later in the Medieval period, but trying to pin down any kind of detail can be frustrating. There's a fairly substantial corpus of textual, archaeological and toponymic evidence that speaks to the cultural significance of horses, but little that might illustrate, for example, how prevalent their ownership was.

Unlike later Medieval - and indeed contemporary continental militaries - the English don't appear to have made use of cavalry in warfare. The Anglo-Saxon Chronicle makes reference to mounted West Saxon men who pursued the defeated Danes and Gaels after the Battle of Brunanburh, but this appears to be a notable exception. Certainly, cavalry is absent from other depictions of battle such as those in Asser's Vita Ælfredi, elsewhere in the ASC or The Battle of Maldon. The ASC itself also takes time to detail that a Danish force which attacked Rocester in the 890s had 'become a mounted force' having captured sufficient horses from the Franks the previous year, but makes no claim to Alfred's army itself taking on a mounted element when it defeats the same army and captures the horses itself. That's not to say that the English didn't use horses in war - there is after all an Old English word specifically for warhorse - but that they rode to battle before fighting on foot.

As we do today, Old English has a number of names for specific types of horse which may illustrate their common uses. Steda, for example is a horse for riding, from which we get the modern 'steed'. Horses weren't generally used in agriculture - contemporary sources place the ox in the role of principle beast of burden - but were used for the movement of people and goods, as well as commonly in entertainment. Bede describes the Anglo-Saxons as being very fond of horse racing, and charter evidence makes reference to specific horse racing tracks. Toponymic evidence suggests that horse breeding was also relatively common. Areas such as Horfield (now a suburb of Bristol but previously Hors-feld) and Studley in Warwickshire (Stod-leah or stud-meadow) are illustrative of a number of sites with toponymic links to horse breeding.

Archaeological evidence is also suggestive of relatively widespread horse ownership, most probably draught animals used by farmers. Horse trappings are among the most common types of early medieval finds listed on the Portable Antiquities Scheme. Stirrups aren't uncommon, but far more common are various elements of horse tack; clasps, buckles, rings and strap ends from various straps and harnesses. The scale of distribution of such finds - largely in a rural context - suggests that horse ownership was relatively commonplace and that horses were used on a regular basis in these contexts.

I cannot answer your historical question but I can add some insight to the modern horse ownership portion you mentioned.

Like to feed it, shelter it, train it, get all the equipment for it etc can't have been cheap but in media it makes horse ownership look like car ownership today, sure some people have better ones but nearly everyone has one.

I would agree that the cost of ownership in those times would not have been cheap. Owners would have been more likely to feed their mounts on fields rather than processed feed like we do today. That means that they would need to own said fields or be traveling.

I would also caution the view of horse ownership the media portrays. Yes, many people have horses and it's not as expensive as it used to be but overall it is still very costly to purchase, feed, shelter, and train one. As a estimate for reference I am someone who has land for my horses and enough experience to be able to train myself, I can also do most vet work myself so I don't really have to worry too much about that cost. Even then the price of a new horse I can ride would be between $2500-$10000, my easy feeder costs around $80-100/month, and I have to pay for hoof trims and shoes every 6 weeks at $100/visit. I have it fairly easy compared to others because I have the experience and land to offset other costs.

Also, thinking about it, horse riding is a skill and not everyone would be able to do it for time or money reasons.

Horse riding is a skill, but riding a decently well trained horse from A to B is not that hard. Plus, most non-experienced people would find themselves able to figure it out easily enough - particularly if the horse was already broken to ride. Except for those people in higher stations that received specific riding instructions I would hazzard a guess that the command layman would not win any prizes for their fancy riding skills. In fact I would probably cringe at the technique they used although it would get the job done (heavy handed on the reins, kicking or squeezing forward while holding the horse back, or punishing the horse for responding to a unintended prompt).

I found this website that does explain horse use during that time, although it doesn't speak to the commonness of horse ownership. http://thethegns.blogspot.com/2012/04/horse.html?m=1