Hello, sorry for the late response as well as a very clumsy writing.

Various sources seem to say that Vikings raiders in England, and later Danish and Norwegian settlers, were seeking more fertile land than that of their cold, rocky, Scandinavian homelands.

First of all, this premise is to much greater extent than generally assumed not accurate.

• At least Western coast of Scandinavian Peninsula is relatively warm thanks for the Gulf Stream (to give some examples, please compare the average temperature by month in Bergen (60.4 degrees in north, Western Norway) and in Tromsø (69.4 degrees in north, Northern Norway) with some cities in Central Europe.
• One of the oldest sources on Viking Age Norway takes a dictation of the narrative of the Norwegian landowner-merchant in Northern Norway who took a visit in the court of King Alfred the Great (r. 871-99) of Wessex. According to the text, this alleged informant, Ohthere (in Old English, usually rendered as Óttar in Old Norse) came from Province Hålogaland in northern Norway, and his wealth was mainly based not solely on land, but also on the special kinds of animals there (reindeer herding and seal -walrus hunting) as well as the trade (tribute taking) with arctic hunter-gathering people called "Finns" (not conflate just with main inhabitants of now Finland, but usually identified with the Sámi people). I cited the excerpt of Ohthere's description on his homeland before here.
• As I explained before in: Do we know how the Anglo-Saxon peasantry felt about the Norse conquests of Britain and subsequent life in the Danelaw?, the current academic consensus does not support the idea of the total population displacement of so-called "Danelaw" region in northern and eastern England. The estimated number of "Danish" (including those who came from now Norway) settlers were supposedly thousands rather than ten thousands, and they tried to settle first in rather later phase (876 in Anglo-Saxon Chronicle).
• Neither did the majority of population probably join in the raiding expeditions either in the British Isles or in Continental Europe (see some answers in: During the "Viking Age", how common was it for Danes, Swedes and Norwegians to become vikingr?......). The raiding was essentially elite and his military retinue's doing (though I don't deny some sporadic raiding by joint-owner of the ships), and their source of wealth, or political economy was based mainly on silver, not just a landed wealth. In other words, the "Viking" chieftain used the successful raid and its loot to earn the loyalty [perhaps as well as more recruits as well] of his military retinue.

Scholarship have tended to emphasize multi-facets aspects of the activity engaged by the Scandinavians abroad in so-called Viking Age around 1970, and these activities are often inter-related each other, and ultimately with the single purpose - to earn the wealth [especially in form of silver] out of their homeland. Chieftain-Merchant Ohthere from northern Norway is reported to present samples of walrus tusk to King Alfred during his stay, and the value of such exotic product / tribute taking of these goods presuppose the Scandinavian external relation with their neighboring people and their markets around western Eurasia.

To give another example, the slave trade conducted by the Vikings is now a popular topic among the researchers, though I suppose the slave hunt must not have been just a sole purpose of raiding. Anyway, Viking "merchants" could get wealth by trading with slaves "somehow" they got somewhere, and the silver hoards discovered across Scandinavia (and also around the Baltic) testify the vast inflow of silvers not only from western Europe, but also (or rather mainly) from the Islamic World where their geographers and diplomats record the arrival of slave traders from northern Europe.

As for more details, please also check my previous posts in: After a successful viking raid, how did all the riches change their life and what did they do with their new found wealth?

While it is very difficult to present the single cause factor of the Viking Age and the weighting among several possible factors vary among the historians (see also this post of a few days ago: Lisbon / Seville were raided by Vikings in 844......), the desire for more fertile land to settle and to cultivate by themselves is most certainly the not prioritized motive for the Scandinavians to go abroad, especially in form of raiders.

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was Denmark not was fertile then?

Basically fertile as it is now, but the landed resource was underutilized even compared with the High Middle Ages later. As I mentioned briefly in What were the societal/religious/political factors that lead to the end of the Viking age?, the end of so-called Viking Age in Scandinavia roughly correspond with the transition to more extensive land use as well as the lordship with now fixed location of settlement, at least in now Denmark. In other words, raiding or going abroad was probably regarded as a more convenient way of getting/ accumulating the wealth for elites in Viking Age Denmark than investing more labor resources in their land.

And if not, could he not just raid South into Germania or the north coast of Poland?

This is indeed a good point. At least two possible factors are related to the relative low interest in Vikings' expansion into these areas.

1. Source Problem!: We have traditionally heavily depended on the writing of Christian clergy and monks on the alleged local impact of the Vikings, and even northern Germany (Saxony) had been christianized only around the beginning of the 9th century - in other words, we don't have much witnesses there, regardless of their trustworthiness.
2. Due to the dearth of large-scale church institutions, these areas might not have been the preferred targets of raiders.
3. Eastward expansion of the Scandinavians in the Viking Age into Russian waterways, heavily based on numismatic evidence, has mainly just attracted much attraction from researchers since the last decades of the 20th century, but not so much out of specialist circles.

These are very rough summaries of my following previous posts:

• What stopped vikings/Norsemen from founding kingdoms and duchies in areas like Germany while they had no trouble doing so in Russia and England?
• Didn’t Vikings raid before they sailed west?

Some recent literature on Early Medieval Poland also suggest that the political re-structure of diverse groups of peoples into the rudimentary statehood of Piast Poland in the 10th century Poland was promoted by their involvement with the global silver-slave trading network in contemporary NW Eurasia that the Vikings also played an important role, as I summarized before in: Where did the Piast dynasty originate from?

If you are interested in literature in individual topics, they'll be found in the linked threads, but I'm also willing to recommend some of them again here (so just ask).